Introduction and Precalculus Blanks - MATH1004D Calculus for Engin or Physics (LEC) Fall 2024 PDF

# Topics and Schedule (Subject to changes and updates over the course of the semester) | Lecture | Topic | Remarks | Textbook reference | |---|---|---|---| | 1 | Precalculus review | Functions, absolute value, inequalities, trig, exp, and log | 1.1-1.4 Appendix A, C | | 2 | Limits | Definitions,...

# Topics and Schedule (Subject to changes and updates over the course of the semester) | Lecture | Topic | Remarks | Textbook reference | |---|---|---|---| | 1 | Precalculus review | Functions, absolute value, inequalities, trig, exp, and log | 1.1-1.4 Appendix A, C | | 2 | Limits | Definitions, computation, limits at infinity | 2.1-2.4 | | 3 | Continuity | Definitions and applications | | | 4 | Derivatives & Techniques | First definitions | 3.1 | | 5 | | Product and Quotient Rules | 3.2 | | 6 | | The Chain Rule | 3.3 | | 7 | | Implicit differentiation | 3.4 | | 8 | | Derivatives of trigonometric functions | 3.5 | | 9 | | Derivatives of exponential functions | 4.3,4.5 | | 10 | | Derivatives of inverse functions. | 3.7-3.9,4,4,4.6 | | 11 | Applications of the derivative | Curve sketching and Optimization | 4.7,5.1-5.3 | | 12 | | L'Hopital rule | 3.10 | | 13 | Integration & Techniques | Anti-derivatives, indefinite integrals | 6.1 | | 14 | | Summation, Definite integrals. | 6.2-6.3 | | 15 | | Area under a curve | 6.4 | | 16 | | U-substitution | 7.2 | | 17 | | U-substitution continued | 7.2 | | 18 | | Integration by parts | 7.3 | | 19 | | Partial Fractions | 7.4 | | 20 | | Trig integration | 7.5 | | 21 | | Trig substitution | 7.6 | | 22 | | Improper integrals | 7.7 | | 23 | | Mixed integral problems | 7.2-7.7 | | 24 | Applications of the integral | Area between curves | 8.2 | | 25 | | Volume of solids of revolution | 8.3 |