2014 January-April

**Instructor:**Balazs Rath

My hand-written, scanned lecture notes

- January 6 lecture (3d space, vectors, plane, normal vector):
- page 1, page 2, page 3.
- In textbook: page 774-775 (ignore "A plane through three points").
- January 8 lecture (parallel planes, orthoganal planes, surfaces, trace of a surface):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 776-781.
- January 10 lecture (cylinders, functions of two variables, domain, range, level curves):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 789-794.
- January 13 lecture (partial derivatives, rate of change, second order partial derivatives, Clairaut):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 810-814.
- January 15 lecture (partial derivative calculations, max/min, critical point def):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 853-854.
- January 17 lecture (saddle point, second derivative test):
- page 1, page 2, page 3, page 4, page 5, page 6, page 7, page 8.
- In textbook: page 855-857.
- January 20 lecture (finding absolute max/min, parametrization of boundary using trigonometric functions):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 858-859.
- January 22 lecture (gradient, method of Lagrange multipliers):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 864-866.
- January 24 lecture (Utility maximization, shortest distances):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 868-869.
- January 27 lecture (sigma notation, summation formulas, area under parabola):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 313.
- January 29 lecture (Regular partition, Riemann sum):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 306-315.
- January 31 lecture (Definite integral, signed area, basic properties, elementary geometry):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 320-331.
- February 3 lecture (Definite integrals, area function, FTC 1, antiderivatives):
- page 1, page 2, page 3, page 4.
- In textbook: page 334-338.
- February 5 lecture (FTC 1 calculations, FTC 2, rules of integration):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 338-345.
- February 7 lecture (substitution rule, integration by parts):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 357-363, page 453-455.
- February 12 lecture (integration by parts, trigonometric integrals):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 455-457, page 460-463.
- February 14 lecture (trigonometric integrals, trig substitutions: sin, tan ):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 460-466, page 468-472.
- February 24 lecture (trig substitutions: sec, completing the square):
- page 1, page 2, page 3, page 4.
- In textbook: page 472.
- February 26 lecture (trig substitutions, rational functions, partial fractions):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 476-479.
- February 28 lecture (partial fractions, repeated linear factors, polynomial division):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 479-480, 482. (ignore "Irreducible Quadratic Factors")
- March 3 lecture (numerical integration: midpoint, trapezoid, Simpson):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 491-498.
- March 5 lecture (Simpson error bound, improper integrals):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 502-509 (ignore volumes of solids of revolution and length of hypocycloid)
- March 7 lecture (improper integrals, differential equations):
- page 1, page 2, page 3, page 4.
- In textbook: page 513.
- March 10 lecture (separable differential equations, first-order linear differential equation with constant coefficients):
- page 1, page 2, page 3, page 4.
- In textbook: page 513-516.
- March 12 lecture (logistic equation, probability theory):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 516-517 (ignore Direction Fields), Probability Appendix: Section 1.1 and 1.2
- March 14 lecture (probability theory: discrete/continuous random variables, cumulative density function):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: Probability Appendix: Section 1.4 and 2.1
- March 17 lecture (probability density function):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: Probability Appendix: Section 2.2
- March 19 lecture (expectation, variance, standard deviation):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: Probability Appendix: Section 2.5 and 2.6
- March 21 lecture (limits of sequences):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 526-530, 537-545 (ignore Formal Definition of a Limit of a Sequence)
- March 24 lecture (geometric, telescopic series):
- page 1, page 2, page 3, page 4.
- In textbook: page 549-553
- March 26 lecture (divergence test, integral test):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 557-564 (ignore Estimating the Value of Series)
- March 28 lecture (comparison test, limit comparison test, ratio test):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 569-575 (ignore Root Test)
- March 31 lecture (power series, center and radius of convergence):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 602-605
- April 2 lecture (representation of functions as a power series, differentiation of power series):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 605-607.
- April 4 lecture (integration of power series, Taylor and MacLaurin):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In textbook: page 607-608, page 611-613.
- April 7 lecture (Taylor and MacLaurin: sin, cos, exp, manipulations):
- page 1, page 2, page 3, page 4, page 5.
- In textbook: page 612-614 (ignore Binomial series and Convergence of Taylor series)