Math 174 – Calculus with Analytic and Geometry II
I. Course Description:
A modern, unified course in analytic
geometry and calculus including indefinite integrals, definite integrals and
their applications, infinite series, conics, parametric equations, vectors, and
functions of several variables.
II. Prerequisites:
MTH
173 - Calculus with Analytic Geometry I.
III. Introduction:
This course is designed to serve as
an introduction to analytic geometry and calculus for students majoring in
mathematics, engineering, computer
science, and science.
IV. Instructional Materials:
Textbook: Calculus,
Eighth Edition, by Larson, Hostetler, and Edwards;Houghton-Mifflin; 2006;
ISBN 0-618-50298-X
Supplementary: Study
and Solutions Guide, Volumes I and II,
by Bruce H. Edwards; ISBN 0-618-52791-5 & 0-618-52792-3
Calculus, 7E, Videotapes by Dana Mosely
Website (college.hmco.com)
Scientific
Calculator
V. References:
Given as necessary.
VI. Course Objectives:
The student must master the
following concepts:
A. Integration
techniques, L'Hopital's rule, and improper integrals (Ch 8)
8.1 Basic integration rules
8.2 Integration by parts
8.3 Trigonometric integrals
8.4 Trigonometric substitution
8.5 Partial fractions
8.6 Integration by tables and other integration
techniques
8.7 Indeterminate forms and L'Hopital's rule
8.8 Improper integrals
B. Infinite series
(Ch 9)
9.1 Sequences
9.2 Series and convergence
9.3 The integral test and p-series
9.4 Comparisons of series
9.5 Alternating series
9.6 The ratio and root tests
9.7
9.8 Power series
9.9 Representation of functions by power series
9.10 Taylor and Maclaurin series
C.
Conics, parametric equations and polar coordinates sections (Ch 10)
10.1 Conics and calculus
10.2 Plane curves and parametric equations
10.3 Parametric equations and calculus
10.4 Polar coordinates and polar graphs
10.5 Area and arc length in polar coordinates
10.6 Polar equations of conics and Kepler's laws
D.
Vectors and the geometry of space (Ch 11)
11.1 Vectors in the plane
11.2 Space coordinates and vectors in space
11.3 The dot product of two vectors
11.4 The cross product of two vectors in space
VII. Suggested weekly outline for Fall and
Spring semesters:
Week 1:
8.1, 8.2
Week 2:
8.3, 8.4
Week 3:
8.5, 8.6
Week 4:
8.7, 8.8
Week 5: T1, 9.1, 9.2
Week 6: 9.3,
9.4
Week 7: 9.5,
9.6
Week 8: 9.7
Week 9: 9.8,
9.9
Week 10: 9.10,
T2, 10.1
Week 11: 10.2,
10.3
Week 12: 10.4, 10.5
Week 13: 10.6,
T3, 11.1
Week 14: 11.2,
11.3
Week 15: 11.4,
T4