Math 175, Spring semester 2019

Calculus II


Math 175 supervisor: Stefan Tohaneanu (email


        Syllabus with tentative schedule of lectures here.

        WebAssign (for online HW) enrollment here. Use the Class Key corresponding to your section (see above). Documentation on student registration here.

        Semester Exams Schedule:

1.     EXAM 1 on Tuesday, January 29, 2019, 7:00pm - 8:00pm

2.     EXAM 2 on Tuesday, February 19, 2019, 7:00pm 8:00pm

3.     EXAM 3 on Tuesday, March 19, 2019, 7:00pm 8:00pm

4.     EXAM 4 on Monday, April 15, 2019, 7:00pm 8:00pm

The exams will take place in the following classrooms:

*    Section 1 in TLC 222

*    Section 2 in TLC 041

*    Section 3 in TLC 022

*    Section 4 in TLC 122


       FINAL EXAM is scheduled for Wednesday, May 8, 2019, 7:00pm 9:00pm in

*  Section 01 in TLC 222

*  Section 02 in TLC 046

*  Section 03 in TLC 022

*  Section 04 in TLC 028





Approved integrals table sheet is here.

Series facts sheet is here.

        EXAM 1

o   Material covered:

        Evaluate values of inverse trigonometric functions. (Section 6.6)

        Calculate derivatives and basic simple integrals involving inverse trigonometric functions. (Section 6.6)

        Evaluate limits of expressions having indeterminate forms (0/0, infinity/infinity, 0*infinity, 1^(infinity), etc.) using L'Hopital's rule. (Section 6.8)

        Evaluate integrals using integration by parts. (Section 7.1)

        Evaluate integrals using partial fractions (Section 7.4). Remember these three cases:

Non-repeated linear factors in the denominator.

A denominator with all linear factors, but some repeated.

A denominator that includes an irreducible quadratic term.

o   Past exams: Exam 1 Fall 2017, Exam 1 Fall 2018, Exam 1 Spring 2019

o   Practice exercises: Practice problems for Exam 1 with solutions.

o   Note: Due to change of textbook, partial fractions (Section 7.4) is taught before trigonometric integrals (Section 7.2) and trigonometric substitution (Section 7.3). For exercises with partial fractions relevant to Exam 1, please check below the past Exams 2, and the practice problems for Exam 2.

        EXAM 2

o   Material covered:

        Evaluate the following types of trigonometric integrals (Section 7.2). Each has a procedure that will work...

Integrals with sines and cosines that include an odd power of one or the other.

Integrals with even powers of sines and cosines.

Integrals with secants and tangents (or cosecants and cotangents) that include an even power of secants (or cosecants).

Integrals with secants and tangents (or cosecants and cotangents) that include an odd power of tangents (or cotangents).

Note: Integrals that have an odd power of secants and an even power of tangents are hard. They can be done using the reduction formulae -- but they will not be included on this exam.

        Evaluate an integral using an appropriate trigonometric substitution. (Section 7.3)

        Be able to choose and apply an appropriate integration strategy (or combination of strategies) for a given integral. (Section 7.5)

        Use the midpoint rule and trapezoid rule to give a numerical estimate of a definite integral. (Note: while we also discussed Simpson's rule, it will not be included on the exam.) (Section 7.7)

        Set up an improper integral as a limit of a definite integral and then evaluate it. (Section 7.8)

o   Past exams: Exam 2 Fall 2017, Exam 2 Fall 2018, Exam 2 Spring 2019

o   Practice exercises: Practice problems for Exam 2 with solutions.


        EXAM 3

o   Material covered:

        Evaluate the limit of a sequence, or show that the limit does not exist. In particular, be able to use the "Squeeze Theorem" to show that a sequence converges. (Section 11.1)

        Be able to write formula for the nth term of a given sequence. (Section 11.1)

        Understand the relationship between an infinite series and the sequence of its partial sums. Be able to describe what it means for series to converge (in terms of the sequence of partial sums). (Section 11.2)

        Calculate the sum of geometric series (or determine that the series diverges). (Section 11.2)

        Calculate the sum of a "telescoping" series. (Section 11.2, page 752)

        Be able to appropriately use the following convergence tests for series:

Divergence Test (Section 11.2)

Integral Test (Section 11.3)

Ratio Test (Section 11.6)

Root Test (Section 11.6)

Comparison Test (Section 11.4)

Limit Comparison Test (Section 11.4)

Alternating Series Test (Section 11.5)

Note: You will be able to use the sheet of series facts.

        Given an infinite series, be able to choose what test is appropriate to use from the above list. (Section 11.7)


o   Past exams: Exam 3 Fall 2017, Exam 3 Fall 2018, Exam 3 Spring 2019

o   Practice exercises: Practice problems for Exam 3 with solutions.

        EXAM 4

o   Material covered:

        Calculate the radius and interval of convergence for a power series. (Section 11.8)

        Create new power series from old ones by combining, integrating, or differentiating. (Section 11.9)

        Calculate the first several terms of the Taylor series for a function at x = a. (Section 11.10)

        Use a Taylor polynomial to approximate a given number (such as e^1/4 or squareroot(4.02)). (Section 11.10)

        Use Taylor's Remainder Theorem to estimate the error in an approximation using a Taylor polynomial. (Section 11.11)

        Use a Taylor series to evaluate a limit. (Section 11.10)

        Use a Taylor series to approximate a definite integral. (Section 11.10)

        Graph a curve given by parametric equations. (Section 10.1)

        Identify a curve from parametric equations by eliminating the parameter to obtain an equation in x and y. (Section 10.1)

        Write parametric equations for a curve of any of the following types: (Section 10.1)

line or segment of a line

circle or arc of a circle

curve given by a functional relationship y = f (x) or x = g(y)

        Calculus with parametric curves: (Section 10.2)



arc length

surface area


o   Past exams: Exam 4 Fall 2017, Exam 4 Fall 2018, Exam 4 Spring 2019

o   Practice exercises: Practice problems for Exam 4 with solutions.

        FINAL EXAM

o   Material covered: topics NOT included in the exam are:

        Approximate integration (Section 7.7)

        Approximation and error estimates using Taylor polynomials (the corresponding material from Sections 11.10 and 11.11)

        Binomial series (the corresponding material from Section 11.10)

        Conic sections (Section 10.4)

o   Past exams: Final Exam Fall 2017, Final Exam Fall 2018

o   Practice exercises: Practice problems for material covered after Exam 4 with solutions.