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Effective: Winter 2015
MATH 1BCALCULUS5 Unit(s)

Prerequisites: Prerequisite: MATH 1A or 1AH.
Advisory: Advisory: Demonstrated proficiency in English by placement as determined by score on the English placement test OR through an equivalent placement process OR completion of ESLL 25 & ESLL 249.
Grade Type: Letter Grade, the student may select Pass/No Pass
Not Repeatable.
FHGE: Communication & Analytical Thinking Transferable: CSU/UC
5 hours lecture. (60 hours total per quarter)

Student Learning Outcomes -
  • A successful student will be able to model, solve, and interpret (in context) application problems involving definite integrals or first order separable differential equations.
  • A successful student will be able to approximate definite integrals and evaluate them exactly, using either areas or the Fundamental Theorem of Calculus, as appropriate.
  • A successful student will be able to understand, interpret, and use appropriate mathematical language and notation when solving integration problems.
Description -
Introduction to integral calculus including definite and indefinite integrals, the first and second Fundamental Theorems and their applications to geometry, physics, and the solution of elementary differential equations.

Course Objectives -
The student will be able to:
  1. Demonstrate an understanding of and evaluate and approximate definite integrals.
  2. Find antiderivatives graphically, and analytically.
  3. Use the First and second Fundamental Theorems of calculus to evaluate definite integrals and construct antiderivatives.
  4. Evaluate a definite integral as a limit.
  5. Apply integration to find area.
  6. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
  7. Apply integration to areas and volumes, and other applications such as work or length of a curve.
  8. Evaluate improper integrals
  9. Graph and integrate functions in polar and parametric forms.
  10. Solve and interpret solutions to elementary differential equations
  11. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (J) above.
  12. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
  13. Interpret mathematical solutions.
Special Facilities and/or Equipment -
A.Graphing Calculator.
  • When taught hybrid: Four lecture hours per week in face-to-face contact and one hour per week using CCC Confer. Students need internet access.

  • Course Content (Body of knowledge) -
    1. Demonstrate an understanding of and evaluate and approximate definite integrals
      1. Signed Area under a curve and the net change of a function F from f.
      2. Properties of integrals
      3. Approximating definite integrals
      4. Interpretations of the definite integral
      5. Average value of a function
      6. Numerical approximations to definite integrals using Rectangular,Trapezoidal and Simpson's approximation and estimation of errors
    2. Find antiderivatives graphically, and analytically
      1. The graphical relationship between a function and its antiderivatives
      2. Construction of antiderivatives analytically
    3. Use the First and Second Fundamental Theorems of calculus to evaluate definite integrals and construct antiderivatives
      1. Fundamental theorem of calculus I for evaluating definite integrals
      2. Fundamental theorem of calculus II for constructing antiderivatives
      3. Fundamental Theorem of calculus for evaluating improper Integrals
    4. Evaluate a definite integral as a limit.
      1. Riemann Sum
    5. Apply integration to find area.
      1. Signed area under a curve
    6. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
      1. Integration by Substitution
      2. Integration by Parts
      3. Integration by Partial Fraction Expansion
      4. Integration using Trigonometric Substitutions
      5. Integrals of inverse functions
      6. Integrals of trigonometric, exponential and logarithmic functions
    7. Apply integration to areas and volumes, and other applications such as work or length of a curve.
      1. Applications of integration to general problems from geometry involving areas, volumes and arc length
      2. Surfaces of revolution
      3. Applications of definite integrals to problems from physics such as work, moments and centers of mass
      4. Applications of integrals to solve simple differential equations of motion
    8. Evaluate improper integrals
      1. Find improper integrals
      2. Interpret improper integrals as families of functions
    9. Graph and integrate functions in polar and parametric forms.
      1. Parametric Curves
      2. Polar Curves
    10. Solve and interpret solutions to elementary differential equations
      1. Verification of solutions to elementary differential equations
      2. Use of slope fields to get qualitative information about solutions to differential equations
      3. Solutions to elementary first order differential equations by separation of variables
      4. Applications of differential equations to growth and decay problems
    11. Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (J) above
      1. Calculator/computer utilities for evaluating definite integrals
      2. Calculator/computer utilities for constructing graphs of antiderivatives
      3. Calculator/computer programs for approximating definite integrals
    12. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
      1. Application problems from other disciplines
      2. Proper notation
    13. Interpret mathematical solutions.
      1. Explain the significance of solutions to application problems.
    Methods of Evaluation -
    1. Written homework
    2. Quizzes & tests
    3. Proctored comprehensive final examination
    Representative Text(s) -
    Stewart, James Calculus: Concepts and Contexts. 4th ed. Belmont, CA, Brooks/Cole, Cengage Learning, 2010.

    Disciplines -
    Mathematics
     
    Method of Instruction -
    Lecture, Discussion, Cooperative learning exercises,
     
    Lab Content -
    Not applicable.
     
    Types and/or Examples of Required Reading, Writing and Outside of Class Assignments -
    1. Homework Problems: Homework problems covering subject matter from text and related material ranging from 30 - 60 problems per week. Students will need to employ critical thinking in order to complete assignments.
    2. Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
    3. Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB.
    4. Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class.