週次 |
授課內容 |
第1週 |
First-Order Linear Differential Equation; The Inverse Trigonometric Functions |
第2週 |
The Derivatives of Inverse Trigonometric Functions; Hyperbolic Functions |
第3週 |
Techniques of Integration; Integration by Parts |
第4週 |
Trigonometric Integrals |
第5週 |
Rationalizing Substitutions ; Integration of Rational Functions |
第6週 |
Rationalizing Substitutions ; Integration of Rational Functions |
第7週 |
Indeterminate Forms; L’Hospital’s Rules |
第8週 |
Cauchy’s Mean Value Theorem; Improper Integrals |
第9週 |
Midterm Exam |
第10週 |
Infinite Series; The Integral Test |
第11週 |
Comparison Test; Ratio Test |
第12週 |
Power Series ; Taylor’s Formula; Taylor and Maclaurin Series |
第13週 |
Vectors; Functions of multiple variables ; Partial Derivatives |
第14週 |
Directional Derivatives and Gradients |
第15週 |
The Chain Rule; Tangent Planes |
第16週 |
Maxima and Minima; Lagrange’s Method |
第17週 |
Double Integrals ; Iterated Integrals |
第18週 |
Final Exam |