Textbook : Calculus(Early Transcendentals), James Stewart, 9th Edition
Sections marked with ◆ are optional and will be covered at the instructor’s discretion. They are not included in the Calculus final exam.
| 10. | Parametric Equations and Polar Coordinates -- 2 hours |
| 10.3 Polar Coordinates | |
| 10.4 Calculus in Polar Coordinates | |
| 11. | Sequences, Series, and Power Series -- 15 hours |
| 11.1 Sequences | |
| 11.2 Series | |
| 11.3 The Integral Test and Estimates of Sums | |
| 11.4 The Comparison Tests | |
| 11.5 Alternating Series and Absolute Convergence | |
| 11.6 The Ratio and Root Tests | |
| 11.7 Strategy for Testing Series | |
| 11.8 Power Series | |
| 11.9 Representations of Functions as Power Series | |
| 11.10 Taylor and Maclaurin Series | |
| 11.11 Applications of Taylor Polynomials | |
| 12.◆ | Vectors and the Geometry of Space -- 1 hours |
| ◆ | 12.1 Three-Dimensional Coordinate Systems |
| ◆ | 12.2 Vectors |
| ◆ | 12.3 The Dot Product |
| ◆ | 12.4 The Cross Product |
| ◆ | 12.5 Equations of Lines and Planes |
| ◆ | 12.6 Cylinders and Quadric Surfaces |
| 13. | Vector Functions -- 3 hours |
| 13.1 Vector Functions and Space Curves | |
| 13.2 Derivatives and Integrals of Vector Functions | |
| 13.3 Arc Length And ◆ Curvature | |
| ◆ | 13.4 Motion in Space: Velocity and Acceleration |
| 14. | Partial Derivatives -- 16 hours |
| 14.1 Functions of Several Variables | |
| 14.2 Limits and Continuity | |
| 14.3 Partial Derivatives | |
| 14.4 Tangent Planes and Linear Approximations | |
| 14.5 The Chain Rule | |
| 14.6 Directional Derivatives and the Gradient Vector | |
| 14.7 Maximum and Minimum Values | |
| 14.8 Lagrange Multipliers | |
| 15. | Multiple Integrals -- 11 hours |
| 15.1 Double Integrals over Rectangles | |
| 15.2 Double Integrals over General Regions | |
| 15.3 Double Integrals in Polar Coordinates | |
| ◆ | 15.4 Application of Double Integrals |
| 15.5 Surface Area | |
| 15.6 Triple Integrals | |
| 15.7 Triple Integrals in Cylindrical Coordinates | |
| 15.8 Triple Integrals in Spherical Coordinates | |
| 15.9 Change of Variables in Multiple Integrals | |
| 16. | Vector Calculus |
| ◆ | 16.1 Vector Fields |
| ◆ | 16.2 Line Integrals |
| ◆ | 16.3 The Fundamental Theorem for line integrals |
| ◆ | 16.4 Green’s Theorem |