Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 1A


COURSE DESCRIPTION
1A Calculus I Units: 4.00
 
Prerequisite(s): MAT 10: Precalculus
Functions, limits, continuity, differentiation, inverse functions, applications of the derivative including maximum and minimum problems, and basic integration. 72 hours lecture and 18 hours laboratory.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
Plane analytic geometry, functions, differentiation with applications and basic integration.
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Solve linear, quadratic, radical, exponential, logarithmic and trigonometric equations.

  2. Graph translations of functions and graphs of conic sections.

  3. Identify the graph of a function from its equation.

  4. Find terms in a geometric and arithmetic sequence and evaluate series.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

1.  Calculate the limit of a function.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

2.  Determine the continuity of a function.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

3.  Find the derivatives of algebraic and transcendental functions.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

4.  Solve related rates problems.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

5.  Apply the absolute and relative extrema to curve sketching and optimization problems.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results

6.  Use Newton’s method to approximate the roots of a function.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

7.  Evaluate a definite integral using Riemann sums.
  

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 

1.   Limits and Rates of Change
      a.   Tangent, velocity and rates of change problems, limits and
            continuity
2.   Derivatives
       a.   Formulas for differentiation, implicit differentiation, higher 
            derivatives, related rates
3.   Inverse Functions and their Derivatives
      a.   Exponential functions, logarithmic functions, inverse
            trigonometric functions, hyperbolic functions, and l’Hospital’s
            Rule
4.         Applications of the Derivative
      a.   Maximum and minimum values, the Mean Value Theorem,
            monotonic functions, concavity, curve sketching, applied 
            maximum and minimum problems
5.   Integrals
      a.   Area under a curve, Riemann Sums, definite integrals, and the
            Fundamental Theorem of Calculus
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Class lectures, discussions, and demonstrations of the limit of a function, continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of curves, using Newton’s method to approximate roots of a function, and evaluating integrals using Riemann sums. 
  • Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist the students in mastering the techniques of determining the limit of a function, determining the continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of curves, using Newton’s method to approximate roots of function, and evaluating integrals using Riemann sums.
  • Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools, manipulatives, and worksheets in order to address multiple learning styles and to reinforce material.
  • Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problem solving skills.
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Write homework assignments and/or computerized homework assignments for correct application of  calculus principles as well as the correct use of symbols and vocabulary of calculus.
  • Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of calculus principles of the limit of a function, continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of curves, using Newton’s method to approximate roots of a function, and evaluating integrals using Riemann sums.
  • Classroom and laboratory discovery activities for content knowledge and conceptual understanding.
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
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:

  • Thomas, George B., et al. Thomas’ Calculus Early Transcendentals. 11th ed. Addison-Wesley, 2005.
  • Smith, Robert and Minton, Roland. Calculus: Early Transcendental Functions. 3rd ed. McGraw Hill, 2006.
  • Stewart, James. Essential Calculus: Early Transcendentals. Brooks/Cole, 2006.
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