# SRJC Course Outlines

 6/8/2023 12:48:48 AM MATH 1B Course Outline as of Fall 2021 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 1B Title:  CALCULUS 2 Full Title:  Calculus, Second Course Last Reviewed:9/14/2020

 Units Course Hours per Week Nbr of Weeks Course Hours Total Maximum 5.00 Lecture Scheduled 5.00 17.5 max. Lecture Scheduled 87.50 Minimum 5.00 Lab Scheduled 0 8 min. Lab Scheduled 0 Contact DHR 0 Contact DHR 0 Contact Total 5.00 Contact Total 87.50 Non-contact DHR 0 Non-contact DHR Total 0

 Total Out of Class Hours:  175.00 Total Student Learning Hours: 262.50

Title 5 Category:  AA Degree Applicable
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:

Catalog Description:
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Topics include methods of integration, conic sections, polar coordinates, infinite sequences and series, parametric equations, solid analytic geometry, and vectors.

Prerequisites/Corequisites:
Completion of MATH 1A or higher (MATH)

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Topics include methods of integration, conic sections, polar coordinates, infinite sequences and series, parametric equations, solid analytic geometry, and vectors.

Prerequisites:Completion of MATH 1A or higher (MATH)
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

 Associate Degree: Effective: Fall 1981 Inactive: Area: BMC Communication and Analytical ThinkingMath Competency CSU GE: Transfer Area Effective: Inactive: B4 Math/Quantitative Reasoning Fall 1981 IGETC: Transfer Area Effective: Inactive: 2A Mathematical Concepts & Quantitative Reasoning Fall 1981 CSU Transfer: Transferable Effective: Fall 1981 Inactive: UC Transfer: Transferable Effective: Fall 1981 Inactive: C-ID: CID Descriptor: MATH 900S Single Variable Calculus Sequence SRJC Equivalent Course(s): MATH1A AND MATH1B CID Descriptor: MATH 230 Multivariable Calculus SRJC Equivalent Course(s): MATH1B AND MATH1C

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Student Learning Outcomes:
At the conclusion of this course, the student should be able to:
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1. Evaluate proper and improper integrals.
2. Define and apply topics from plane analytic geometry including polar and parametrically defined graphs, conic sections, and vectors.
3. Define and apply topics from solid analytic geometry including quadric surfaces, lines and planes in space, and vectors.
4. Determine convergence of sequences and series, and compute and use power series of elementary functions.

Objectives: Untitled document
Students will be able to:
1.   Apply methods of integration, including integration by parts, integrals of inverse functions, trigonometric substitutions and partial fractions, to calculate proper and improper integrals.
2.   Define and discuss conic sections as equations, as geometric intersections and as loci.
3.   Apply differentiation and integration to parametric representations of graphs, including polar graphs.
4.   Use three dimensional rectangular coordinates.
5.   Determine convergence of sequences and series.
6.   Compute power series of functions, their derivatives and integrals.
7.   Compute Taylor and Maclaurin series and demonstrate applications to elementary functions.
8.   Determine radii and intervals of convergence of power series.
9.   Compute and use determinants, dot products, cross products, and projections.
10. Determine lines and planes in space.
11. Describe velocity and acceleration of particles in the plane and in space using vector functions.

Topics and Scope
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I. Integration
A. Integration by parts
B. Integration of inverse functions
C. Trigonometric integrals
D. Trigonometric substitutions
E. Partial fractions
F. Improper integrals
G. Area of surfaces of revolution

II. Topics From Plane Analytic Geometry
A. Conic sections
B. Polar coordinates and graphs

III. Infinite Series
A. Sequences and series
B. Convergence tests
C. Power series
D. Radii and intervals of convergence
E. Taylor polynomials and approximations
F. Derivatives and integrals of power series
G. Taylor and Maclaurin series

IV. Parametric Equations
A. Tangents, arc length and areas
B. Tangents and area for polar graphs

V. Topics from Solid Analytic Geometry
A. Rectangular coordinate system

VI. Vectors
A. Vectors in the plane and in space
B. Determinants
C. Dot and cross products
D. Projections
E. Lines and planes in space
F. Differentiation and integration of vector valued functions
G. Velocity and acceleration
H. Tangent and normal vectors
I.  Curvature

Assignments:
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1. Daily reading outside of class (20-50 pages per week)
2. Problem set assignments from required text(s) or supplementary materials chosen by the instructor (1-6 per week)
3. Quizzes (0-4 per week)
4. Exams (2-7 per term)
5. Final Exam
6. Projects (for example, computer explorations or modeling activities, 0-10 per term)