Math 153 (sequence)

I have taught the in-sequence Math 153 (third quarter calculus, covering advanced integration techniques, differential equations, sequences, and series leading up to Taylor series and power series) three times. The first time, in Spring 2010, I taught it as the third quarter of a three-quarter calculus sequence (151-2-3). I later taught the class in Winter 2011 and Winter 2012 as the second of a two-quarter sequence (152-3). All the courses covered roughly the same material in the same order. I am including the lecture notes and materials for the most recent incarnation of the course. For the standalone version of the course, see Math 153 (standalone). The materials have substantial overlap but are covered in a somewhat different order. Also, the standalone Math 153 was taught later and the quizzes on the same topics sometimes have more and better questions; cases where this happens are indicated.

Alternative learning recommendations

If you’re interested in recommendations for learning single-variable calculus, see Cognito Mentoring’s single-variable calculus learning recommendations page, to which I was a primary contributor.


The textbook for the course was Calculus: One Variable (Tenth Edition) by Salas, Hille, and Etgen. In the lecture notes and quizzes, it may occasionally be referred to as the “book” or “textbook” or “text” — however, it is not necessary to buy or own the book in order to make sense of the lecture notes or quizzes. The book is not very different from other standard calculus texts such as the book by Stewart.

Lecture notes plus quizzes plus videos

On the topics for which videos exist, the videos were created after the last time I taught the course, and were therefore not available to students.

For solutions to any quiz, add -solns to the part of the URL just before the .pdf at the end of the URL. For instance, the solutions file for the quiz with URL has URL

Some video links are pending.

Notes Sections in textbook (Salas et al) Related quiz(zes) Related video(s)
Exponential growth 7.6 Exponential growth
Inverse trigonometric functions 7.7 Inverse trigonometric functions
Hyperbolic functions 7.8 Hyperbolic functions
Integration by parts 8.2, parts of 8.3 Integration by parts (updated standalone class quiz) Playlist
Induction 1.8 Induction
Integrating radicals 8.4 Partial fractions and radicals (combined with next topic)
Partial fractions: an integrationist perspective 8.5 Partial fractions and radicals (combined with previous topic) Playlist
Differential equations 9.1, 9.2 Differential equations

Playlists: basic, advanced
Improper integrals 11.7 Limits at infinity and improper integrals
Least upper bound axiom 11.1 — (quiz in standalone version)
Sequences of real numbers 11.2 Sequences and miscellanea (pending)
Continuous and discrete: the interplay Interplay of continuous and discrete (pending)
Convergence of sequences 11.3 (see quizzes above on sequences) Playlist
Limit computation techniques 11.4, 11.5, 11.6 Limits, order of zero, and L’Hopital’s rule (pending)
Series and convergence 12.1, 12.2, 12.3 Sequences and series (miscellaneous stuff) Related: degree difference test playlist
Root and ratio tests 12.4 Series (shared with next) (see previous)
Absolute and conditional convergence 12.5 Series (shared with previous) Alternating series and Riemann series rearrangement theorem playlist
Taylor polynomials and Taylor series 12.6, 12.7 Taylor series and power series (shared with next) Playlist
Power series and convergence issues 12.8, 12.9 Taylor series and power series (shared with previous) Playlists: Power series summation and Taylor series, rules for determining interval of convergence
Summation techniques odds and ends from Chapter 12 (pending)

Quizzes reviewing prior material

Mixed bowl of hard nuts contains some of the hardest problems on the material people are expected to know coming into this class.

Review sheets

Basic review sheets are unions of executive summaries of the corresponding lecture notes. Advanced review sheets include error-spotting exercises and other practice material.

Review sheet for … Sections of book covered
midterm 1 (basic) 7.6-7.8, 8.2-8.3, 1.8
midterm 1 (advanced) 7.6-7.8, 8.2-8.3, 1.8
midterm 2 (basic) 8.4-8.5, 9.1-9.2, 11.1-11.7
midterm 2 (advanced) 8.4-8.5, 9.1-9.2, 11.1-11.7
final (basic) 12.1-12.9
final (advanced) 12.1-12.9

Basic information