Santa Barbara City College Course Outline

MATH 160C - Support Course for Calculus with Analytic Geometry II

MATH 160C
Support Course for Calculus with Analytic Geometry II
Disciplines
Mathematics (Masters Required)
2.000
0 - May not be repeated
A review of core prerequisite skills, competencies, advanced algebra and beginning calculus concepts for second semester calculus. Intended for students who are concurrently enrolled in Math 160 Calculus with Analytic Geometry II at Santa Barbara City College. Review topics include skills developed in college algebra, precalculus, and first-semester calculus, with an emphasis on refining skills in algebraic manipulation, functions, trigonometry, proofs, limits and differentiation.
32.000-36.000 Total Hours
Total Hours
64.000-72.000 Total Hours
32.000-36.000 Total Hours
Prerequisite: None
Prerequisite or Corequisite: None
Concurrent Corequisite: MATH 160
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Graph functions using methods of calculus
Solve advanced algebraic and trigonometric functions.
Use trigonometry in simple applications such as triangle solving problems, polar coordinates, parametric equations, and vectors in two dimensions.
Analyze and solve problems involving algebraic fundamentals, functions, graphs, and trigonometric functions.
Compute derivatives using differentiation formulas and use differentiation to solve applications.
Analyze and manipulate symbolically expressions representing sequences and series.
Student Learning Outcomes
MATH160C SLO1 - Use a problem solving process to extract relevant information and execute relevant advanced algebraic, trigonometric, and beginning calculus calculations/simplifications.
MATH160C SLO2 - Interpret results derived from advanced algebraic, trigonometric, and beginning calculus calculations relevant to the solution of a problem.

This support course will cover a SUBSET of these topics in just-in-time remediation for success in the Math 160 Calculus and Analytical Geometry I course:

  1. Develop study habits that promote success in Math 160, such as the use of test preparation and metacognitive strategies to improve understanding and performance.

2. Functions and graphing

    1. Graphs of rational functions, exponential functions, log functions

    2. Graphs of all six trigonometric functions including period changes, amplitude changes, and shifts

    3. Graphs of arcsine, arccosine, arctangent functions

    4. Graphs of polar functions

    5. Graphs of parametrically defined curves

    6. Calculator usage with respect to graphs


3.  Trigonometry

a. Review of unit circle

b.. Trig Inverse values

c. Right triangle trigonometry,

d. compositions of trig and trig inverses, creating algebraic expressions involving x

e .Trigonometric identities (Statements and proofs)


4.  Algebra

    1. Laws of logarithms and exponents

    2. Simplifying with factorials

    3. Polynomial Long-division

    4. Partial Fractioning


5. Geometry

  1. Writing algebraic expressions for areas and volumes of common geometric shapes

  2. Writing algebraic expressions using similar triangles and right triangle trigonometry

  3. Circumference of a circle, area of a sector of a circle


6. Sequences and Series

  1. Sequence and summation notation, including developing a formula for a sequence or series/pattern recognition, standard conventions.

  2. Arithmetic and geometric sequences and series, including modeling a word problems with a series


7. Logic and Proof

  1. Review of if-then statements, if-and-only-if statements.

  2. Converse, inverse, and contrapositive.

  3. Induction.


8 Vectors

  1. 2d-vector representations (componentwise, direction/magnitude, between two points)

  2. Vector plotting

  3. Vector algebra

  4. Applications of vectors (simple work problems assuming a constant force)


9. Calculus I

  1. Limits, in particular limits at infinity, including techniques such as squeeze theorem and L’Hospital’s Rule as well a graphically and algebraically.

  2. Physical Interpretation of derivative: slope of the tangent line and instantaneous rate  of change.

  3. Differentiation rules and techniques

  4. Mean Value Theorem (derivative form)

  5. Simple differential equations and  initial value problems (such as f ''=2x+sin(x), f(0)=2, f '(0)=1)

  6. Common antiderivatives  and guess and check integrating

  7. Integral techniques: substitution and integration by parts

  8. Definition of definite Integral (as limit of a Riemann Sum) and area interpretation

  9. Midpoint Rule for approximating a definite integral

  10. The Fundamental Theorem of Calculus (both parts)



Methods of Instruction
Directed Study
Discussion
Lecture
Student activities, groupwork, and computer-facilitated instruction (optional).
Find the general antiderivatives for the following functions: x sin(x), x cos(x), x tan(x), and x sec(x).
A. Writing Assignments: Students must work on assigned mathematical problems requiring the manipulation of abstract symbols. B. Appropriate Outside Assignments: Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete homework assignments. C. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills such as equation solving and graphing which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. Critical thinking will also be emphasized through numerous treatments of word problems.
A grading system will be established by the instructor and implemented uniformly. Grades will be based on demonstrated proficiency in subject matter determined by multiple measurements for evaluation, one of which must be essay exams, skills demonstration or, where appropriate, the symbol system. 1)Independent exploration activities which measure students’ ability to analyze the connections between the numeric, algebraic, and verbal representations of various types of algebraic expressions, equations, graphs when applied to real-world problems and data analysis. 2)Quizzes and exams (including a comprehensive in-class final exam) which measure students’ ability to work independently using graphic, numeric, and algebraic techniques. 3)Homework in which students apply graphic, numeric and algebraic principles discussed in class to a series of practice problems to help them formulate questions and receive feedback from the instructor, tutors, or classmates. 4)(Optional) Computer laboratory assignments in which students apply algebraic principles and problem-solving techniques discussed in class to help students identify gaps in their skill attainment and concept mastery and to improve their symbolic manipulation abilities and problem-solving skills. Out-of-Class Assignments 1)Problem sets 2)Exploratory activities and/or projects 3)Reading and/or writing assignments
  • Projects/activities created by SBCC Math faculty.
10/06/2018
Board of Trustees: 12/13/2018
CAC Approval: 11/19/2018