# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 21B: Calculus: Integral Calculus
Approved: 2007-04-01 (revised 2013-01-01, J. DeLoera)

ATTENTION:

This course is part of the inclusive access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Thomas' Calculus Early Transcendentals, 14th Edition by George B. Thomas, Maurice Weir, and Joel Hass; Addison Wesley Publishers.

Prerequisites:

MAT (21A or MAT 21AH) with a C- or above; or 17A with B or above.

Suggested Schedule:

 Lecture(s) Sections Comments/Topics 1 4.8 Antiderivatives 1 5.1 Area and estimating with finite sums 1 5.2 Sigma notation and limits of finite sums 1 5.3 The definite integral 1.5 5.4 The Fundamental Theorem of Calculus 1 5.5 Indefinite integrals and the substitution method 1 5.6 Substitution and area between curves 1.5 6.1 Volumes using cross sections 1 6.2 Volumes using cylindrical shells 1 6.3 Arc length 1 6.4 Areas of surfaces of revolution 1 6.5 Work and fluid forces 1 6.6 Moments and centers of mass 1 7.1 The logarithm defined as an integral 2 7.2 Exponential change and separable differential equations 1 8.1 Integration by parts 1 8.2 Trigonometric integrals 1 8.3 Trigonometric substitutions 1 8.4 Integration of rational functions by partial fractions 1 8.7 Numerical integration 1 8.8 Improper integrals 0.5 11.1 Parametrization of plane curves 1 11.2 Calculus with parametric curves 0.5 11.3 Polar coordinates 1 11.4 Graphing in polar coordinates

Total number of lectures = 26. This leaves time for exams and time adjustments. If time permits, one lecture on section 10.6 (graphing in polar coordinates), one lecture on 10.7 (area in polar coordinates), and two lectures on section 9.1 (Slope fields and Separable differential equations).

Learning Goals:

A goal of this course is to help students develop effective strategies for solving both mathematical and real world problems. Although students often do not like “word problems” probing applications of their mathematical skills, it is very important that instructors emphasize these types of problems so that students become experts at them. In particular, students should be taught how to create mathematical models, develop effective strategies for solving problems in applied settings and non-routine situations.

Students will learn the fundamentals of integral calculus. The course begins with the integral of a continuous function defined as the limit of its Riemann sum before the Fundamental Theorems of Calculus presents integrals as anti-derivatives. Integrals are applied to many problems in physics, including area, volume, arc length, surface area, and center of gravity. Various techniques of integration are studied and include u-substitution, integration by parts, integration by partial fractions, and trigonometric substitution. After applying integrals to separable differential equations, the course concludes with the calculus of parametric equations.

This course is a pre-requisite for multi-variable and vector calculus. Mastery of this course would be manifested in improved reading, writing, thinking, and problem solving skills. Students should have an increased ability to understand, visualize, categorize, model, and solve complicated calculus problems in both two- and three-dimensional space.

Assessment:

Mastery of this course is usually assessed by periodic quizzes, homework problems, TA led discussion sections, hour exams, and a comprehensive final exam.