This companion book to Thinkwell's Calculus course is an optional resource to complement the video lessons in Thinkwell Calculus.
Preface | 9 |
1. About OpenStax | 9 |
2. About OpenStax's resources | 9 |
3. About Calculus Volume 1 | 9 |
4. Additional resources | 11 |
5. About the authors | 12 |
Chapter 1. Functions and Graphs | 15 |
1.1. Review of Functions* | 16 |
1.2. Basic Classes of Functions* | 44 |
1.3. Trigonometric Functions* | 70 |
1.4. Inverse Functions* | 86 |
1.5. Exponential and Logarithmic Functions* | 104 |
Glossary | 125 |
Chapter 2. Limits | 131 |
2.1. A Preview of Calculus* | 132 |
2.2. The Limit of a Function* | 143 |
2.3. The Limit Laws* | 168 |
2.4. Continuity* | 187 |
2.5. The Precise Definition of a Limit* | 202 |
Glossary | 216 |
Chapter 3. Derivatives | 221 |
3.1. Defining the Derivative* | 222 |
3.2. The Derivative as a Function* | 240 |
3.3. Differentiation Rules* | 255 |
3.4. Derivatives as Rates of Change* | 274 |
3.5. Derivatives of Trigonometric Functions* | 285 |
3.6. The Chain Rule* | 295 |
3.7. Derivatives of Inverse Functions* | 307 |
3.8. Implicit Differentiation* | 317 |
3.9. Derivatives of Exponential and Logarithmic Functions* | 327 |
Glossary | 342 |
Chapter 4. Applications of Derivatives | 349 |
4.1. Related Rates* | 350 |
4.2. Linear Approximations and Differentials* | 362 |
4.3. Maxima and Minima* | 374 |
4.4. The Mean Value Theorem* | 387 |
4.5. Derivatives and the Shape of a Graph* | 398 |
4.6. Limits at Infinity and Asymptotes* | 415 |
4.7. Applied Optimization Problems* | 447 |
4.8. L’Hôpital’s Rule* | 462 |
4.9. Newton’s Method* | 480 |
4.10. Antiderivatives* | 493 |
Glossary | 507 |
Chapter 5. Integration | 515 |
5.1. Approximating Areas* | 516 |
5.2. The Definite Integral* | 537 |
5.3. The Fundamental Theorem of Calculus* | 557 |
5.4. Integration Formulas and the Net Change Theorem* | 574 |
5.5. Substitution* | 592 |
5.6. Integrals Involving Exponential and Logarithmic Functions* | 603 |
5.7. Integrals Resulting in Inverse Trigonometric Functions* | 616 |
Glossary | 624 |
Chapter 6. Applications of Integration | 631 |
6.1. Areas between Curves* | 632 |
6.2. Determining Volumes by Slicing* | 644 |
6.3. Volumes of Revolution: Cylindrical Shells* | 664 |
6.4. Arc Length of a Curve and Surface Area* | 679 |
6.5. Physical Applications* | 693 |
6.6. Moments and Centers of Mass* | 711 |
6.7. Integrals, Exponential Functions, and Logarithms* | 729 |
6.8. Exponential Growth and Decay* | 742 |
6.9. Calculus of the Hyperbolic Functions* | 753 |
Glossary | 764 |
Appendix A. Table of Integrals* | 771 |
A.1. Basic Integrals | 771 |
A.2. Trigonometric Integrals | 771 |
A.3. Exponential and Logarithmic Integrals | 773 |
A.4. Hyperbolic Integrals | 773 |
A.5. Inverse Trigonometric Integrals | 773 |
A.6. Integrals Involving a2 + u2, a > 0 | 774 |
A.7. Integrals Involving u2 − a2, a > 0 | 774 |
A.8. Integrals Involving a2 − u2, a > 0 | 775 |
A.9. Integrals Involving 2au − u2, a > 0 | 775 |
A.10. Integrals Involving a + bu, a ≠ 0 | 776 |
Appendix B. Table of Derivatives* | 777 |
B.1. General Formulas | 777 |
B.2. Trigonometric Functions | 777 |
B.3. Inverse Trigonometric Functions | 777 |
B.4. Exponential and Logarithmic Functions | 778 |
B.5. Hyperbolic Functions | 778 |
B.6. Inverse Hyperbolic Functions | 778 |
Appendix C. Review of Pre-Calculus* | 779 |
C.1. Formulas from Geometry | 779 |
C.2. Formulas from Algebra | 779 |
C.3. Formulas from Trigonometry | 780 |
Solutions | 783 |
Chapter 1 | 783 |
Chapter 2 | 797 |
Chapter 3 | 806 |
Chapter 4 | 823 |
Chapter 5 | 835 |
Chapter 6 | 852 |
Index | 873 |
CalculusVolume1.pdf | 2 |
Blank Page | 2 |
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