A youtube Calculus Workbook (Part I)
Publisher: Bookboon.com
Published: 2013
Table of contents: title: Contenido; title: 1. M1: Limits; title: 1.1. Definition of the limit of a function; title: 1.2. Limit laws; title: 1.3. Evaluating limits; title: 1.4. Squeeze Theorem; title: 1.5. Applications; title: 1.6. M1 Sample Quiz; title: 1.7. Solutions to M1 sample Quiz; title: 2. M2: One-sided limits; infinite limits and limits at infinity; title: 2.1. one-sided limits: definition; title: 2.2. one-sided limits: examples; title: 2.3. M2 Sample Quiz 1: one-sided limits; title: 2.4. Solutions to the M2 sample Quiz; title: 2.5. Definition of infinite limits; title: 2.6. Finding vertical asymptotes; title: 2.7. Limits at infinity and horizontal asymptotes; title: 2.8. Finding horizontal asymptotes; title: 2.9. Slant asymptotes; title: 2.10. 1M2 sample Quiz 2: infinite limits, limits at infinity, asymptotes; title: 2.11. 1Solutions to the M2 sample Quiz; title: 3. M3: Continuity and Derivatives; title: 3.1. Continuity: definition; title: 3.2. Finding discontinuities; title: 3.3. The Intermediate Value Theorem; title: 3.4. M3 Sample Quiz 1: continuity; title: 3.5. M3 Sample Quiz 1 Solutions; title: 3.6. Definition of the derivative; title: 3.7. Derivative as a function; title: 3.8. Derivative: Examples and applications; title: 3.9. M3 Sample Quiz 2: derivative; title: 3.10. 1M3 Sample Quiz 2 Solutions; title: 4. Review for the first 3 modules; title: 4.1. MOCK TEST; title: 4.2. Solutions to Mock Test; title: 5. M4: Differentiation Rules; title: 5.1. Power Rule for differentiation; title: 5.2. Constant multiple and Sum Rules for derivatives; title: 5.3. Product Rule for differentiation; title: 5.4. Quotient Rule for derivatives; title: 5.5. Differentiation Rules, examples and applications; title: 5.6. M4 Sample Quiz; title: 5.7. M4 Sample Quiz Solutions; title: 6. M5: Derivatives of Trigonometric functions; Chain Rule; title: 6.1. Derivatives of trig functions; title: 6.2. Derivatives of trig functions: Examples; title: 6.3. M5 Sample Quiz 1: derivatives of trig functions; title: 6.4. M5 Sample Quiz 1 Solutions; title: 6.5. Chain Rule; title: 6.6. Examples using the Chain Rule; title: 6.7. M5 Sample Quiz 2: Chain Rule; title: 6.8. M5 Sample Quiz 2 Solutions; title: 7. M6: Implicit Differentiation; Related Rates Problems; title: 7.1. Implicit Differentiation; title: 7.2. Implicit Differentiation: Examples; title: 7.3. M6 Sample Quiz 1: Implicit Differentiation; title: 7.4. M6 Sample Quiz 1 Solutions; title: 7.5. Related Rates: first problems; title: 7.6. Related Rates: filling up a tank; title: 7.7. Related Rates: Radar gun; title: 7.8. Related Rates: moving shadow; title: 7.9. M6 Sample Quiz 2: Related Rates; title: 7.10. 1M6 Sample Quiz 2 Solutions; title: 8. Review on modules M4 to M; title: 8.1. MOCK TEST; title: 8.2. MOCK TEST 2 Solutions; title: 9. M7: Extreme Values of a function; title: 9.1. Extrema; title: 9.2. local extrema and critical values; title: 9.3. Closed Interval Method; title: 9.4. M7 Sample Quiz; title: 9.5. M7 Sample Quiz Solutions; title: 10. M8: the Mean Value Theorem and first derivative Test; title: 10.1. Rolle’s Theorem; title: 10.2. The Mean Value Theorem; title: 10.3. Applications of the Mean Value Theorem; title: 10.4. M8 Sample Quiz 1: Mean Value Theorem; title: 10.5. M8 Sample Quiz 1 Solutions; title: 10.6. Intervals of increase and decrease; title: 10.7. First Derivative Test: further examples; title: 10.8. M8 Sample Quiz 2: Intervals of increase and decrease; title: 10.9. M8 Sample Quiz 2 Solutions; title: 11. M9: Curve Sketching; title: 11.1. Concavity and inflection points; title: 11.2. Second derivative Test; title: 11.3. Curve Sketching: Examples; title: 11.4. M9 Sample Quiz: Curve Sketching; title: 11.5. M9 Sample Quiz Solutions; title: 12. M10: Optimization; title: 12.1. Optimization: First examples and general method; title: 12.2. Example: an open box; title: 12.3. Example: the best poster; title: 12.4. Example: across the marshes; title: 12.5. Example: the best soda can; title: 12.6. M10 Sample Quiz: optimization; title: 12.7. M10 sample Quiz Solutions; title: 13. Review on modules 7 through 1; title: 13.1. MOCK TEST; title: 13.2. MOCK TEST 3 Solutions; title: 14. M11: Definite Integral; title: 14.1. Preliminaries: Sums; title: 14.2. The area problem; title: 14.3. Formal definition of the definite integral; title: 14.4. First examples of definite integrals; title: 14.5. Properties of integrals; title: 14.6. M11 Sample Quiz; title: 14.7. M11 Sample Quiz Solutions; title: 15. M12: Indefinite Integral; title: 15.1. Antiderivatives; title: 15.2. Antiderivatives: Examples; title: 15.3. M12 Sample Quiz: indefinite integrals; title: 15.4. M12 Sample Quiz Solutions; title: 16. M13: Calculating Integrals; title: 16.1. Fundamental Theorem of Calculus; title: 16.2. Proof of the Fundamental Theorem of Calculus; title: 16.3. M13 Sample Quiz 1: FTC applied; title: 16.4. M13 Sample Quiz 1 Solutions; title: 16.5. Substitution for indefinite integrals; title: 16.6. Substitution for definite integrals; title: 16.7. Integrals and symmetry; title: 16.8. M13 Sample Quiz 2: substitution; title: 16.9. M13 Sample Quiz 2 Solutions; title: 17. M14: areas and other applications; title: 17.1. Area between two curves; title: 17.2. M14 Sample Quiz 1: areas; title: 17.3. M14 Sample Quiz 1 Solutions; title: 17.4. Arc Length; title: 17.5. Work; title: 17.6. M14 Sample Quiz 2: applications; title: 17.7. M14 Sample Quiz 2 Solutions; title: 18. M15: Volumes; title: 18.1. Volume by cross-section; title: 18.2. Volume by cross-section: solids of revolution; title: 18.3. Volume by cylindrical Shells; title: 18.4. M15 Sample Quiz: volumes; title: 18.5. M15 Sample Quiz Solutions; title: 19. Review on Modules 11 through 1; title: 19.1. MOCK TEST; title: 19.2. MOCK TEST 4 Solutions; title: 20. Index; title: 21. Endnote