[major=IA | course_id=MAE101 | syllabus_id=13137 | semester=1 | combo=core | title=Mathematics for Engineering]
Course ID: MAE101
Title EN: Mathematics for Engineering
Title VI: Toán cho ngành kỹ thuật
Credits: 3.0
Prerequisites: 
Description: Upon finishing the course, students must acquire:
1. the following knowledge: (ABET a1)
• The basic concepts of single variable calculus: limit, derivative, integral.
• Concepts of linear system of equations, matrix and their applications
• The concepts of vector spaces, basis and dimension, linear transformations and their applications.
• The range of application of calculus and algebra in science, technology, economics & finance...
2. the following skills: (ABET a2)
• Find limit, derivative and integral of functions of single variables;
• Find solutions to linear systems by using row-reduced echelon form, Cramer's Rule, inverse matrix
• Find determinants and inverse of a matrix
• Find linear transformations in R^2 and R^3.
• Find dimensions and bases of vector spaces .
• Apply the concepts of calculus and algebra in solving problems in science, technology, economics & finance, ...
Student tasks: Students must attend at least 80% of contact hours in order to be accepted to the final examination.
Tools: 
Course type: traditional
Decision: 932/QĐ-ĐHFPT dated 08/22/2025
Approved date: 2025-08-22
CLO1: Describe basic properties and find the limit of a function LO1.1 Find the domain, range, zeros and analyze the symmetry of the graph; create new functions from old functions. LO1.2 Find the slope and write an equation of a line; describe how a function changes under graph translations. LO1.3 Compute the limit of a function using graphs and limit laws, including the Squeeze's Theorem. LO1.4 Find limits at infinity and infinity limits, and apply in finding asymptotes of a function. LO1.5 Identify where a function is continuous; use the Intermedia Value Theorem to show that an equation has a solution.
[1] category=Assignments/Exercises; type=on-going; weight=30.0; duration=3 hours; question_type=LO1, LO2, LO3, LO4, LO5, LO6, LO7, LO8, LO9; grading_guide=Assignment 1 covers Chapters 1, 2, 3, 4 (Vol.1), 1, 3 (Vol.2) - Calculus ; Assignment 2 covers Chapters 1, 2, 3 (Linear algebra) ; Assignment 3 covers Chapters 4, 5 (Linear algebra); completion_criteria=; clos=>0
[2] category=Progress Test; type=on-going; weight=30.0; duration=OP1: Test 1: 40'; Test 2&3: 30' // OP2: (For Constructivism Approach only): Follow lecturer's proposal; question_type=LO1, LO2, LO3, LO4, LO5, LO6, LO7, LO8, LO9; grading_guide=Test 1 covers Chapters 1, 2, 3, 4 (Vol.1), 1, 3 (Vol.2) - Calculus ; Test 2 covers Chapters 1, 2, 3 (Linear algebra) ; Test 3 covers Chapters 4, 5 (Linear algebra); completion_criteria=; clos=>0
[3] category=Final Exam; type=Final exam; weight=40.0; duration=60'; question_type=; grading_guide=All studied chapters. Each studied Chapter contributes 2-8 questions, depending on the number of topics in the Chapter.; completion_criteria=; clos=4
[1] desc=Calculus 1; author=; publisher=; edition=; isbn=; main=True; online=True; note=https://openstax.org/details/books/calculus-volume-1
[2] desc=Calculus 2; author=; publisher=; edition=; isbn=; main=True; online=True; note=https://openstax.org/details/books/calculus-volume-2
[3] desc=powerpoint in CD + Powerpoint prepared by previous lecturers (PP).; author=; publisher=; edition=; isbn=; main=; online=; note=
[4] desc=Student Video Skillbuilder in CD (Video).; author=; publisher=; edition=; isbn=; main=; online=; note=
[5] desc=Animation in CD (Animation).; author=; publisher=; edition=; isbn=; main=; online=; note=
[6] desc=Computerized tools (for example Maxima http://maxima.sourceforge.net/) (CT); author=; publisher=; edition=; isbn=; main=; online=; note=
[7] desc=Essential Calculus; author=James Stewart; publisher=Thomson Brooks/Cole; edition=; isbn=978-0-495-10860-3; main=; online=; note=
[8] desc=Calculus for engineers; author=Donald Trim; publisher=Prentice Hall,; edition=; isbn=0-13-085603-7; main=; online=; note=
[9] desc=Calculus; author=Stanley I. Grossman; publisher=; edition=; isbn=0-03-096420-2; main=; online=; note=
[10] desc=Linear Algebra with applications; author=W.Keith Nicholson,; publisher=Mc Graw Hill Education; edition=; isbn=987-1-259-07299-4.; main=; online=; note=
[11] desc=Linear Algebra with Applications; author=W. Keith Nicholson; publisher=Lyryx Online Resources; edition=2021-A; isbn=; main=True; online=True; note=https://lyryx.com/linear-algebra-applications/
[12] desc=Coursera - FPT University Private Authored Courses: Linear transformation with python (Guided Project); author=; publisher=; edition=; isbn=; main=; online=True; note=Optional practice
Session 1: 0 Introduction.
1.1 Review of Functions.
1.2 Basic Classes of Functions
Topic: Offline; Teaching type: LO1; LO: ITU
ITU: Textbook Chapter 1
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 1(Calculus Vol. 1)

Session 2: 2.1 A Preview of Calculus.
2.2 The Limit of a Functions
Topic: Offline; Teaching type: LO1; LO: TU
ITU: Textbook Chapter 2
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 2(Calculus Vol. 1)

Session 3: 2.3 The Limit Laws
2.4 Continuity
Topic: Offline; Teaching type: LO1; LO: TU
ITU: Textbook Chapter 2
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 2(Calculus Vol. 1)

Session 4: 3.1 Defining the Derivative
3.2 The Derivative as a Function
Topic: Offline; Teaching type: LO2; LO: IT
ITU: Textbook Chapter 3
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 3(Calculus Vol. 1)
CLO2: Calculate derivatives of a function LO2.1 Find the average rate of change; identify derivative as the limit of a difference quotient. LO2.2 Recognize derivative as the instantaneous velocity and the slope of tangent lines. LO2.3 Find derivatives using basic formulas and the sum, difference, product, quotient, chain rules.
Session 1: 3.3 Differentiation Rule.
3.4 Derivatives as Rates of Change
3.5 Derivatives of Trigonometric Functions
Topic: Offline; Teaching type: LO2; LO: TU
ITU: Textbook Chapter 3
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 3(Calculus Vol. 1)

Session 2: 3.6 The Chain Rule. 3.8 Implicit Differentiation
Topic: Offline; Teaching type: LO2; LO: TU
ITU: Textbook Chapter 3
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 3(Calculus Vol. 1)

Session 3: 3.9 Derivatives of Exponential and Logarithmic Functions
Topic: Offline; Teaching type: LO2; LO: TU
ITU: Textbook Chapter 3
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 3(Calculus Vol. 1)

Session 4: 4.1 Related Rates
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 4
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 4(Calculus Vol. 1)
CLO3: Use derivatives to analyze a function and to solve applications LO3.1 Use implicit differentiation to find derivatives and to solve related rates problems. LO3.2 Find linear approximation of a function; calculate differentials and apply in calculating errors of approximation. LO3.3 Apply Rolle's Theorem and Mean Value Theorem to a function; find critical numbers and absolute extrema of a function. LO3.4 Identify local extrema, and describe the monotonicity of a function; solve optimization problems. LO3.5 Recognize acceleration as second derivative; determine inflection points and describe the concavity of a function. LO3.6 Use Newton method to approximate solutions of an equation.
Session 1: 4.2 Linear Approximations and Differentials
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 4
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 4(Calculus Vol. 1)

Session 2: 4.3 Maxima and Minima
4.4 The Mean Value Theorem
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 4
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 4(Calculus Vol. 1)

Session 3: 4.5 Derivatives and the Shape of a Graph
4.6 Limits at Infinity and Asymptotes
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 4
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 4(Calculus Vol. 1)

Session 4: 4.7 Applied Optimization Problems
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 4
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 4(Calculus Vol. 1)
CLO4: Calculate integrals and find area under the graph of a function LO4.1 Use Riemann sums to approximate area; recognize area as a definite integral which is the limit of Riemann sums. LO4.2 Apply the Fundamental Theorems of Calculus to find derivatives of integrals, and to evaluate definite integrals. LO4.3 Recognize indefinite integrals as anti-derivatives; find integrals using basic formulas and the techniques of substitution and integration by parts. LO4.4 Use integration to solve applications and to compute the average value of a function. LO4.5 Approximate definite integrals using Midpoint, Trapezoidal and Simpson rules. LO4.6 Determine if an improper integral converges.
Session 1: 4.9 Newton's Method
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 4
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 4(Calculus Vol. 1)

Session 2: 4.10 Antiderivatives
Topic: Offline; Teaching type: LO3; LO: TU
ITU: Textbook Chapter 4
(Calculus Vol. 1)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 4(Calculus Vol. 1)

Session 3: 1.1 Approximating Areas
Topic: Offline; Teaching type: LO4; LO: IT
ITU: Textbook Chapter 1
(Calculus Vol. 2)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 1(Calculus Vol. 2)

Session 4: 1.2 The Definite Integral
1.3 The Fundamental Theorem of Calculus
Topic: Offline; Teaching type: LO4; LO: IT
ITU: Textbook Chapter 1
(Calculus Vol. 2)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 1(Calculus Vol. 2)
CLO5: Solve a system of linear equations using Gaussian elimination LO5.1 Identify if a matrix is in echelon forms; carry a matrix into an echelon using row operations; calculate the rank of a matrix. LO5.2 Use echelon matrices to solve/describe the solution set of a linear system.
Session 1: 1.4 Integration Formulas and the Net Change Theorem
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 1
(Calculus Vol. 2)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 1(Calculus Vol. 2)

Session 2: 1.5 Substitution
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 1
(Calculus Vol. 2)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 1(Calculus Vol. 2)

Session 3: 3.1 Integration by Parts 3.6 Numerical Integration
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 3
(Calculus Vol. 2)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 3 (Calculus Vol. 2)

Session 4: 3.7 Improper integrals
Topic: Offline; Teaching type: LO4; LO: TU
ITU: Textbook Chapter 3
(Calculus Vol. 2)
Download: https://flm.fpt.edu.vn/gui/role/student/Exercises Chapter 3 (Calculus Vol. 2)
CLO6: Perform basic operations on matrices and manipulate matrix transformations LO6.1 Perform addition, scalar multiplication and transpose of matrices; verify if a matrix is symmetric. LO6.2 Multiply two matrices of appropriate sizes; transform between a linear system and a matrix equation. LO6.3 Determine the matrix of a linear transformation; use properties of linear transformations in solving problems.
Session 1: Review
Topic: Offline; Teaching type: LO1, LO2, LO3, LO4; LO: U
ITU: 

Session 2: Progress Test 1
Topic: Offline; Teaching type: LO1, LO2, LO3, LO4; LO: U
ITU: 

Session 3: 1.1 Solutions of Systems of Linear Equations
Topic: Offline; Teaching type: LO5; LO: IT
ITU: Textbook Chapter 1 (Linear Algebra)
Download: Exercises Chapter 1 (Linear Algebra)

Session 4: 1.1 Elementary Operations
Topic: Offline; Teaching type: LO5; LO: TU
ITU: Textbook Chapter 1 (Linear Algebra)
Download: Exercises Chapter 1 (Linear Algebra)
CLO7: Find the determinant, inverse and diagonalization of a matrix LO7.1 Compute the cofactors and the determinant of a matrix; analyze determinants in relation with row/column operations. LO7.2 Check if a matrix is invertible; find the adjugate and the inverse of a matrix; use properties of inverses and determinants in solving problems. LO7.3 Solve a system of linear equations using inverse matrices or Cramer's rule. LO7.4 Find the characteristic polynomial, eigenvalues and eigenvectors to diagonalize a matrix; check if a matrix is diagonalizable.
Session 1: 1.2 Gaussian Elimination
Topic: Offline; Teaching type: LO5; LO: TU
ITU: Textbook Chapter 1 (Linear Algebra)
Download: Exercises Chapter 1 (Linear Algebra)

Session 2: 1.3 Homogeneous Equations
Topic: Offline; Teaching type: LO5; LO: TU
ITU: Textbook Chapter 1 (Linear Algebra)
Download: Exercises Chapter 1 (Linear Algebra)

Session 3: 2.1 Matrix Addition, Scalar Multiplication, and Transposition
Topic: Offline; Teaching type: LO6; LO: TU
ITU: Textbook Chapter 2 (Linear Algebra)
Download: Exercises Chapter 2 (Linear Algebra)

Session 4: 2.2 Matrix-Vector Multiplication
Topic: Offline; Teaching type: LO6; LO: TU
ITU: Textbook Chapter 2 (Linear Algebra)
Download: Exercises Chapter 2 (Linear Algebra)
CLO8: Manipulate vector operations and linear transformations in R^3. LO8.1 Manipulate vector operations; find equations of lines. LO8.2 Compute the dot product and the angle between two vectors; find the projection of a vector on another vector and manipulate equations of planes. LO8.3 Compute the cross product; analyze areas and volumns in relation with dot and cross products. LO8.4 Determine linear transformations in R^3 and discuss applications in computer graphic.
Session 1: 2.2 Matrix Transformations
Topic: Offline; Teaching type: LO6; LO: TU
ITU: Textbook Chapter 2 (Linear Algebra)
Download: Exercises Chapter 2 (Linear Algebra)

Session 2: 2.3 Matrix multiplication
Topic: Offline; Teaching type: LO6; LO: TU
ITU: Textbook Chapter 2 (Linear Algebra)
Download: Exercises Chapter 2 (Linear Algebra)

Session 3: 2.4 Matrix Inverses
Topic: Offline; Teaching type: LO6; LO: TU
ITU: Textbook Chapter 2 (Linear Algebra)
Download: Exercises Chapter 2 (Linear Algebra)

Session 4: 2.4 Properties of Inverses
Topic: Offline; Teaching type: LO6; LO: TU
ITU: Textbook Chapter 2 (Linear Algebra)
Download: Exercises Chapter 2 (Linear Algebra)
CLO9: Find the dimension and bases of a subspace LO9.1 Determine if a subset of vectors is a subspace; describe the subspace spanned by a set of vectors. LO9.2 Check if a set of vectors are independent; determine if a set of vectors form a basis. LO9.3 Find a basis and the dimension of a subspace; analyze the rank in relation with the dimension of the column, row and the null space of a matrix. LO9.4 Compute dot product and length of vectors; check if a set of vectors are orthogonal or orthonormal; write a vector as a linear combination of an orthogonal basis.
Session 1: 2.6 Linear Transformations
Topic: Offline; Teaching type: LO6; LO: TU
ITU: Textbook Chapter 2 (Linear Algebra)
Download: Exercises Chapter 2 (Linear Algebra)

Optional Practice:
Coursera - FPT University Private Authored Courses: Linear transformation with Python (Guided Project)

Session 2: 3.1 The Cofactor Expansion
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 3 (Linear Algebra)
Download: Exercises Chapter 3 (Linear Algebra)

Session 3: 3.1 Properties of Determinants
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 3 (Linear Algebra)
Download: Exercises Chapter 3 (Linear Algebra)

Session 4: 3.2 Determinants and Matrix Inverses
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 3 (Linear Algebra)
Download: Exercises Chapter 3 (Linear Algebra)
Session 1: 3.2 Cramer's Rule
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 3 (Linear Algebra)
Download: Exercises Chapter 3 (Linear Algebra)

Session 2: 3.3 Eigenvalues and Eigenvectors
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 3 (Linear Algebra)
Download: Exercises Chapter 3 (Linear Algebra)

Session 3: 3.3 Diagonalization
Topic: Offline; Teaching type: LO7; LO: TU
ITU: Textbook Chapter 3 (Linear Algebra)
Download: Exercises Chapter 3 (Linear Algebra)

Session 4: Review
Topic: Offline; Teaching type: LO5, LO6, LO7; LO: U
ITU:
Session 1: Progress Test 2
Topic: Offline; Teaching type: LO5, LO6, LO7; LO: U
ITU: 

Session 2: 4.1 Vectors
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)

Session 3: 4.1 Lines in Space
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)

Session 4: 4.2 Projections
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)
Session 1: 4.2 Planes
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)

Session 2: 4.2 Cross Product
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)

Session 3: 4.3 More on the Cross Product
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)

Session 4: 4.4 Linear Operations on R^3
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)
Session 1: 4.4 Transformations of Areas and Volumes
Topic: Offline; Teaching type: LO8; LO: TU
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)

Session 2: 4.5 An application in Computer Graphics
Topic: Offline; Teaching type: LO8; LO: IT
ITU: Textbook
Chapter 4
(Linear Algebra)
Download: Textbook
Chapter 4
(Linear Algebra)

Session 3: 5.1 Subspaces of R^n
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)

Session 4: 5.1 Spanning Sets
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)
Session 1: 5.2 Linear Independence
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)

Session 2: 5.2 Dimension
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)

Session 3: 5.3 Dot Product, Length, and Distance
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)

Session 4: 5.3 Orthogonal Sets and the Expansion Theorem
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)
Session 1: 5.4 Rank of a Matrix
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)

Session 2: 5.4 Rank, Nullity, and Linear Systems
Topic: Offline; Teaching type: LO9; LO: TU
ITU: Textbook Chapter 5 (Linear Algebra)
Download: Exercises Chapter 5 (Linear Algebra)

Session 3: Review
Topic: Offline; Teaching type: LO8, LO9; LO: U
ITU: 

Session 4: Progress Test 3
Topic: Offline; Teaching type: LO8, LO9; LO: U
ITU: