# Math 152H, Fall 2008

## Course Materials

Schedule and Homework (Updated Daily)

## Past Exams

Here are some exams from when I last taught Math 151H and 152H. Note that the syllabus changed somewhat since then, so the particular topics covered are somewhat different now compared to then. Also some of the Math 151 material got moved to Math 152 and vice versa. However the style of the exams will be similar to the ones here.
Final for Math 151H (pdf)
Exam 2 for Math 152H (pdf)
Exam 3 for Math 152H (pdf)
Final for Math 152H (pdf)

## Project One

The project should be done in groups of two. One project write-up per group.
Project 1 (pdf)
MyFunction.m
Examples.m
Matlab Tutorial

## Info Re Exam One

Exam One will cover 4.1-4.7.

About 10%-15% of the exam will directly test theory we have studied in the course. In particular you should know the following definitions and theorems.
Antiderivative, indefinite integral, Theorem 1.1 p345, indefinite integrals on pages 347, 349
Theorem 2.1 p 356
Definitions of area under curve, Riemann sum, left endpoint, right endpoint, midpoint sums, definite integral, signed and total areas
Theorem 4.1 and 4.2 on p 375, Theorem 4.3 on page 377
FTC versions I and II in Section 4.5
Trapezoid and Simpson's Rule
Know how to use and apply the error bound theorems on pages 410 411 (Theorems 7.1, and 7.2). However if I ask about them I will give statements of the formulae in the exam.
Finally you should be able to prove the two versions of the FTC with the level of rigor we used in class.

Solutions to Exam One (pdf)

## Project Two

The project should be done in groups of two. One project write-up per group.

Project 2 will be handed out in class
The following two matlab functions will be helpful for the Project and for the homework on arclength.
MidpointSum.m
ArcLengthExample.m

## Info Re Exam Two

Exam Two will cover 4.8, 5.1, 5.2, 5.3, 5.4, 9.1, 9.2, 9.3, 6.1, 6.2.

You should know the following definitions and theorems.
Definition of ln(x) in terms of an integral.
How to work out graph of y=ln(x) from this defintion.
Log Laws and their proofs (Theorem 8.1, section 4.8)
Definition of the number e and the function exp
Proof that derivative of exp(x) is exp(x).
Defintion of a^x and proof of formula for derivative of a^x.
I will not test theory from chapters 5,6,9 but you need to know the formulae for finding volumes, surface areas, arc lengths etc. so you can solve problems.

## Project Three

The project should be done in groups of two. One project write-up per group.

Project Three [pdf]

## Info Re Exam Three

Exam Three will cover 6.3, 6.4, 6.6, 8.1, 8.2, 8.3 (Integral Test only)
Theory: Definition of impropoer integrals; result that if intgerals is convergent then function converges to 0; comparison theorm for improper integrals; definitions of infinite sequences and series; formal definition of and picture for limit of sequence; Theorems 1.2, 1.3, 1.4 and Definitions 1.3 1.4 in Section 8.1; Section 8.2: Theorem 2.1, 2.2; Section 8.3: Theorems 3.1, 3.2, p-series result on page 639.

## Info Re Final Exam

The Final Exam covers all material in the course. In addition to the sections listed above for Exams 1,2,3 the folowing sections will be covered:
8.3-8.7
More weight will be placed on material covered since the 3rd exam. More info on that later.

In addition to the theory topics listed for the first 3 exams you should now the following: Section 8.3: Thms 3.3, 3.4; Sec 8.4: Thms 4.1, 4.2; Sec 8.5: Defn of absolute and conditional convergence, Thms 5.1, 5.2, 5.3. The Summary table on page 663 is useful! Sec 8.6: Def of power series and the ideas behind Fig 8.38, Thm 6.1 and how to calculate radius of convergence using ratio/root tests. Result on differentiating and integrating power series pn page 668 and fact that radius of convergence of derivative and intergal is same as that of original power series. Sec 8.7: Def of taylors series and formula for coefficients in terms of derivatives of f(x). How to compute taylors series of functions like exponetials, logs, sin, cos, Thms 7.1 and 7.2;