LECTURE NOTES ON CALCULUS (DREXEL 2005-2006)
1. Derivatives, Integrals and the Fundamental Theorem of Calculus (A Brief Aerial View of the Terrain)
3. Limits (Intuitive Approach)
4. Techniques for Computing Limits I
5. Techniques for Computing Limits II
7. Limits of Trigonometric Functions (The Squeeze Theorem)
8. Tangent Lines and Rates of Change
10. Differentiation Techniques
11. Derivatives of Trigonometric Functions
12. The Chain Rule
14. Local Linear Approximation
16. Derivatives of Logarithmic, Exponential and Inverse Trigonometric Functions
17. L'Hôpital's Rule
18. Increasing, Decreasing, Concavity
20. Absolute Maxima and Minima
21. Applied Maximum-Minimum Problems
22. Newton's Method
27. Integration by Substitution
29. Fundamental Theorem of Calculus
31. Definite Integrals by Substitution
32. Mass and Areas Between Curves
33. Volumes I
34. Volumes II
35. Arc Length
36. Work and Energy
38. Hyperbolic Form of the Lorentz Transformations and "Addition of Velocities"
39. Basic Integration Techniques
42. Trigonometric Substitution
45. Introduction to Ordinary Differential Equations
46. Geometrical and Numerical Methods
48. Second Order Linear Differential Equations
49. Polynomial Approximation of Functions
52. Infinite Series
54. Series of Non-Negative Terms
56. Power Series
57. Convergence of Taylor Series
58. Differentiation and Integration of Series
59. Series Solutions of Differential Equations
62. Cartesian Coordinates in 3-Space
64. Functions of Two or More Variables
65. Limits and Continuity for Multivariable Functions
67. Chain Rule for Multivariable Functions
68. Introduction to Partial Differential Equations