Math 222  Schedule
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Schedule is only tentative. Use of this page may cause lightheadedness, growth of hair on the palms, and/or world peace.
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Week 1 
I. Methods of Integration 
§1. Definite and indefinite integrals 
§3. First trick: using the double angle formulas 

Week 2 
§5. Integration by Parts 
§6. Reduction Formulas 
§8. Partial Fraction Expansion 

Week 3 
§10. Substitutions for integrals containing the expression $\sqrt {ax^2+bx+c}$ 
§11. Rational substitution for integrals containing $\sqrt {x^2a^2}$ or $\sqrt {a^2+x^2}$ 
§12. Simplifying $\sqrt {ax^2+bx+c}$ by completing the square 

Week 4 
II. Proper and Improper Integrals 
§1. Typical examples of improper integrals 
§2. Summary: how to compute an improper integral 
§3. More examples 
§5. Estimating improper integrals 

Week 5 
III. First order differential Equations 
§1. What is a Differential Equation? 
§2. Two basic examples 
Exam 1 

Week 6 
§3. First Order Separable Equations 
§5. First Order Linear Equations 

Week 7 
§7. Direction Fields 
§8. Euler's method 
§10. Applications of Differential Equations 

Week 8 
IV. Taylor's Formula 
§1. Taylor Polynomials 
§2. Examples 
§3. Some special Taylor polynomials 

Week 9 
§5. The Remainder Term 
§6. Lagrange's Formula for the Remainder Term 



Week 10 
§8. The limit as $x\to 0$, keeping $n$ fixed 
§10. Differentiating and Integrating Taylor polynomials 
§12. Proof of Theorem . . . 
§13. Proof of Lagrange's formula for the remainder 

Week 11 
Exam 2 
V. Sequences and Series 
§1. Introduction 
§2. Sequences 

Week 12 
§4. Series 
§5. Convergence of Taylor Series 
§7. Leibniz' formulas for $\ln 2$ and $\pi /4$ 

Week 13 
VI. Vectors 
§1. Introduction to vectors 
§2. Geometric description of vectors 
§3. Parametric equations for lines and planes 
§4. Vector Bases 

Week 14 
§5. Dot Product 
§6. Cross Product 

Week 15 
§7. A few applications of the cross product 
§8. Notation 
