Discipline: Mathematics
Originator: Veasna Chiek

# Riverside Community College District Integrated Course Outline of Record

Mathematics 1C
 MAT-1C : Calculus III College: RIV MOV NOR Lecture Hours: 72.000 Lab Hours: 18.000 Outside-of-Class Hours: 144.000 Units: 4.00 Grading Methods: Pass/No Pass Letter Grade
Course Description
Prerequisite: MAT-1B
Course Credit Recommendation: Degree Credit

Vectors in a plane and in space, vector functions, calculus on functions of multiple variables, partial derivatives, multiple integrals, line and surface integrals, Green's theorem, Stokes' theorem, Divergence theorem, and elementary applications to the physical and life sciences. 72 hours lecture. 18 hours lab.
Short Description for Class Schedule
Vectors, partial differentiation, and multiple integrals with applications.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
1. Evaluate definite, indefinite, and improper integrals.
• MAT-1B - Evaluate definite, indefinite, and improper integrals.
2. Graph, differentiate, and integrate functions in polar and parametric form.
• MAT-1B - Graph, differentiate, and integrate functions in polar and parametric form.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
1. Perform and apply vector operations.
2. Determine equations of lines, planes and surfaces.
3. Find the limit of a function at a point.
4. Evaluate derivatives.
5. Write the equation of a tangent plane at a point.
6. Determine differentiability.
7. Find local extrema and test for saddle points.
8. Solve optimization problems using the method of the Lagrange multipliers.
9. Find the divergence and curl of a vector field.
10. Evaluate double and triple integrals.
11. Apply Green's, Stokes', and Divergence theorems.
12. Technology-based analysis of level curves, surfaces, vector fields and iterated integrals using either a Computer Algebra System (CAS) or a Software Programming Language (SPL).

Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
1. Apply vector value functions to analyze the motion of an object in space.
• Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
2. Solve optimization problems and find extrema for functions of several variables.
• Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
3. Evaluate double and triple integrals to solve applications involving area, mass, and volume.
• Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
Course Content:
1. Vectors and vector operations in two and three dimensions
1. Dot, cross, and triple products; projections
2. Vector and parametric equations of lines and planes
3. Rectangular equations of a plane; surfaces in space
4. Polar, cylindrical, and spherical coordinates
2. Vector-valued functions
1. Differentiation and integration
2. Arc length and curvature
3. Velocity and acceleration
4. Tangent, normal, and binormal vectors
5. Tangent planes, normal planes, and binormal planes
3. Functions of several variables
1. Level curves and surfaces
2. Limits, continuity, and their properties
3. Differentiability and differentiation
4. Partial derivatives, chain rule, higher-order derivatives
5. Differentials
7. Local and absolute maxima and minima
9. Lagrange multipliers
4. Multiple integration and applications
1. Double and triple integrals,
2. Area and volume
3. Center of mass and centroids
4. Moments of inertia
5. Jacobian; change of variables theorem
6. Integration in polar, cylindrical, and spherical coordinates
5. Vector analysis
1. Vector fields
2. Gradient vector field and conservative fields
3. Parametrically defined surfaces
4. Line integrals and surface integrals
5. Divergence and curl
6. Green’s, Stokes', and Divergence theorems
6. Programming CAS (computer Algebra System) and or a SPL (Software Programming Language)
1. Graph of surfaces, level curves and vector fields
2. Differentiation
3. Integration
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
• Class lectures, discussions, and demonstrations of vector operations, determining equations of lines and planes, finding the limit of a function at a point, evaluating derivatives, writing the equation of a tangent plane at a point, determining differentiability, finding local extrema and testing for saddle points, solving constraint problems using Lagrange multipliers, computing arc length, finding the divergence and curl of a vector field, evaluating iterated integrals, and applying Green's, Stokes' and divergence theorems.
• Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist students in mastering the techniques involved in determining equations of lines and planes, finding the limit of a function at a point, evaluating derivatives, writing the equation of a tangent plane at a point, determining differentiability, finding local extrema and testing for saddle points, solving constraint problems using Lagrange multipliers, computing arc length, finding the divergence and curl of a vector field, evaluating iterated integrals, and applying Green's, Stokes' and divergence theorems.
• Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools such as a CAS (Computer Algebra System) and/or a SPL (Software Programming Language), manipulatives, and worksheets in order to address multiple learning styles and to reinforce concepts of vector calculus.
• Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problem-solving skills in the field of multivariable calculus.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
• Written homework assignments and/or computerized homework assignments designed to assess the correct application of multivariable calculus principles and use of its symbols and vocabulary.
• Quizzes, midterms, and final examinations designed to assess conceptual understanding and correct techniques and applications of calculus principles to vector operations, determining equations of lines and planes, finding the limit of a function at a point, evaluating derivatives, writing the equation of a tangent plane at a point, determining differentiability, finding local extrema and testing for saddle points, solving constraint problems using Lagrange multipliers, computing arc length, finding the divergence and curl of a vector field, evaluating iterated integrals, applying Green's, Stokes' and Divergence theorems.
• Classroom and laboratory discovery activities designed to promote content knowledge and conceptual understanding of vector calculus, such as calculating the flux through a surface using the Divergence Theorem paired with the aide of a CAS (Computer Algebra System) and/or a SPL (Software Programming Language) for complicated integrated integrals.
Sample Assignments:
• Students are expected to read and analyze the text and study lecture notes covering topics such as limits, partial differentiation, iterated integrals, surface integrals, and Divergence Theorem.
• Students are expected to be able to read and analyze the lecture notes on how to use a CAS (Computer Algebra System) and/or a SPL (Software Programming Language).
Outside-of-Class Writing Assignments
• Demonstrate critical thinking skills by analyzing and solving constraint problems with the use of Lagrange multipliers or other using the concepts and techniques of multivariable calculus.
• Students are able to demonstrate the use of a CAS (Computer Algebra System) and/or a SPL (Software Programming Language) when analyzing iterated integrals.
Other Outside-of-Class Assignments
• Problem sets that require students to solve applications with the use of double and triple integrals, graph quadric surfaces and vector fields, and apply Green's, Stokes', and Gauss' Theorem.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
• Edwin Herman and Gilbert Strange. Calculus Volume 3. OpenStax, 2016.
• Larson and Edwards. Multivariable Calculus. 11th Cengage Learning , 2017.
• Stewart, J.. Calculus, Multivariable. 8th Cengage Learning, 2015.
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
C-ID#: MATH 230
Board of Trustees Approval Date: 01/15/2019
COR Rev Date: 01/15/2019