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1131 M05-09 |
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| Calculus 1 |
Week 1 |
2.1 |
The Tangent and Velocity Problems |
Worksheet 1 (Inverse Trigonometric Functions) |
| 2.2 |
The Limit of a Function |
| 2.3 |
Calculating Limits Using the Limit Laws |
| Week 2 |
2.5 |
Continuity |
Worksheet 2 (The Precise Definition of a Limit) |
| 2.6 |
Limits at Infinity; Horizontal Asymptotes |
| 2.7 |
Derivatives and Rates of Change |
| Week 3 |
2.8 |
The Derivative as a Function |
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| 3.1 |
Derivatives of Polynomials and Exponential Functions |
| 3.2 |
The Product and Quotient Rules |
| 3.3 |
Derivatives of Trigonometric Functions |
| Week 4 |
3.4 |
The Chain Rule |
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| 3.5 |
Implicit Differentiation |
| 3.6 |
Derivatives of Logarithmic and Inverse Trigonometric Functions |
| 3.10 |
Linear Approximations and Differentials |
| Week 5 |
4.1 |
Maximum and Minimum Values |
Worksheet 3 (Related Rates) |
| 4.2 |
The Mean Value Theorem |
| 4.3 |
What Derivatives Tell Us about the Shape of a Graph |
Week 6
10/11(Fri) Calculus 1 Drop Deadline |
4.4 |
Indeterminate Forms and l'Hospital's Rule |
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| 4.5 |
Summary of Curve Sketching |
| Week 7 |
4.7 |
Optimization Problems |
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| 4.9 |
Antiderivatives (*) |
| Week 8 |
Buffer |
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| 10/26(Sat) Exam |
| Calculus 2 |
Week 9
11/1(Fri) Calculus 2 Withdrawal Deadline |
5.1 |
The Area and Distance Problems |
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| 5.2 |
The Definite Integral |
| 5.3 |
The Fundamental Theorem of Calculus |
| 5.4 |
Indefinite Integrals and the Net Change Theorem |
| Week 10 |
5.5 |
The Substitution Rule |
Worksheet 1 (Volumes) |
| 6.1 |
Areas Between Curves |
| 7.1 |
Integration by Parts |
| Week 11 |
7.2 |
Trigonometric Integrals |
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| 7.3 |
Trigonometric Substitution |
Week 12
11/22(Fri) Calculus 2 Drop Deadline |
7.4 |
Integration of Rational Functions by Partial Fractions |
Worksheet 2 (Other Applications) |
| 7.5 |
Strategy for Integration |
| Week 13 |
7.8 |
Improper Integrals |
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| 8.5 |
Probability |
| Week 14 |
9.1 |
Modeling with Differential Equations |
Worksheet 3 (More on Probability) |
| 9.3 |
Separable Equations |
| 9.5 |
Linear Equations |
| Week 15 |
Buffer |
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| 12/14(Sat) Exam |
| Week 16 |
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1132 M05-09 |
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| Calculus 3 |
Week 1 |
12.6 |
Cylinders and Quadric Surfaces |
Worksheet 1 (Space Curves and Their Tangents) |
| 14.1 |
Functions of Several Variables |
| 14.2 |
Limits and Continuity |
| 14.3 |
Partial Derivatives |
| Week 2 |
14.4 |
Tangent Planes and Linear Approximations |
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| 14.5 |
The Chain Rule |
| Week 3 |
14.6 |
Directional Derivatives and the Gradient Vector |
Worksheet 2 (Polar Coordinates) |
| 14.7 |
Maximum and Minimum Values |
| Week 4 |
14.8 |
Lagrange Multipliers |
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| 15.1 |
Double Integrals over Rectangles |
| Week 5 |
15.2 |
Double Integrals over General Regions |
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| 15.3 |
Double Integrals in Polar Coordinates |
Week 6
3/28(Fri) Calculus 3 Drop Deadline |
15.6 |
Triple Integrals |
Worksheet 3 (Applications of Double Integrals) |
| 15.7 |
Triple Integrals in Cylindrical Coordinates |
| 15.8 |
Triple Integrals in Spherical Coordinates |
| Week 7 |
15.9 |
Change of Variables in Multiple Integrals |
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| Week 8 |
Buffer |
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| 4/12(Sat) Exam |
| Calculus 4 |
Week 9
4/18(Fri) Calculus 4 Withdrawal Deadline |
16.1 |
Vector Fields |
Worksheet 1 (Parametric Surfaces) |
| 16.2 |
Line Integrals |
| 16.3 |
The Fundamental Theorem for Line Integrals |
| Week 10 |
16.4 |
Green's Theorem |
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| 16.5 |
Curl and Divergence |
| Week 11 |
16.6 |
Parametric Surfaces and Their Areas |
Worksheet 2 (More on Conservative Fields) |
| 16.7 |
Surface Integrals |
Week 12
5/9(Fri) Calculus 4 Drop Deadline |
16.8 |
Stokes' Theorem |
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| 16.9 |
The Divergence Theorem |
| 11.1 |
Sequences (*) |
| Week 13 |
11.2 |
Series |
Worksheet 3 (Convergence Tests) |
| 11.3 |
The Integral Test and Estimates of Sums |
| 11.4 |
The Comparison Tests (Skip the Limit Comparison Test) |
| 11.5 |
Alternating Series and Absolute Convergence |
| Week 14 |
11.6 |
The Ratio and Root Tests |
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| 11.8 |
Power Series |
| 11.9 |
Representations of Functions as Power Series |
| Week 15 |
11.10 |
Taylor and Maclaurin Series |
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| Bonus Introduction to Multivariable Taylor Series (*) |
| Week 16 |
Buffer |
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| 6/7(Sat) Exam |