# Math 222 - Schedule

Schedule is only tentative. Use of this page may cause lightheadedness, growth of hair on the palms, and/or world peace. No guarantees, void where prohibited.

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 $\sqrt {x^2-a^2}$ 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
 SPRING BREAK
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