Discipline: Mathematics
Originator: Amanda Brown

Riverside Community College District
Integrated Course Outline of Record

Mathematics 1A
MAT-1A : Calculus I
College:
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-10 or MAT-23 or qualifying placement level.
Course Credit Recommendation: Degree Credit

Functions, limits, continuity, techniques and applications of differentiation, the Fundamental Theorem of Calculus, and basic integration. 72 hours lecture and 18 hours laboratory. (Letter Grade or Pass/No Pass option)
Short Description for Class Schedule
Differentiation with applications and basic integration.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. Solve algebraic, exponential, logarithmic and trigonometric equations.
    • MAT-10 - Solve algebraic, exponential, logarithmic, and trigonometric equations and algebraic inequalities.
    • MAT-23 - Solve algebraic, exponential, logarithmic, and trigonometric equations and algebraic inequalities using appropriate techniques.
  2. Graph algebraic, exponential, logarithmic and trigonometric functions.
    • MAT-10 - Graph translations of algebraic, exponential, logarithmic, and trigonometric functions and identify the graph of a function from its equation.
    • MAT-23 - Graph algebraic, exponential, logarithmic and trigonometric functions.
  3. Manipulate and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
    • MAT-10 - Manipulate and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
    • MAT-23 - Manipulate and simplify algebraic, exponential, logarithmic, and trigonometric expressions.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Compute the limit of a function at a real number.
  2. Determine if a function is continuous at a real number.
  3. Find the derivative of a function as a limit.
  4. Find the equation of a tangent line to a function.
  5. Compute derivatives using differentiation rules.
  6. Use implicit differentiation.
  7. Use differentiation to solve applications such as related rate and optimization problems.
  8. Graph functions using methods of calculus.
  9. Evaluate definite integrals using the limit definition.
  10. Use the Fundamental Theorem of Calculus to evaluate integrals.
  11. Apply integration to find area.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Compute the limit of a function.
    • 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. Find the derivative of a function.
  3. Use differentiation to solve applications.
    • 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.
  4. Evaluate integrals.
Course Content:
  1. Limits
    1. Tangent and velocity problems
    2. Definition of limit
    3. Computation using numerical, graphical, and algebraic approaches
    4. Continuity of functions
    5. Indeterminate forms and L'Hospital's Rule
  2. Derivatives
    1. Differentiability of functions
    2. Derivative as a limit
    3. Interpretation of the derivative
      1. Slope of tangent line
      2. Rate of change 
    4. Differentiation formulas
      1. Constants
      2. Power rule
      3. Product rule
      4. Quotient rule
      5. Chain rule
    5. Derivatives of transcendental functions such as trigonometric, exponential, and logarithmic functions 
    6. Implicit differentiation
    7. Differentiation of inverse functions
    8. Related rates
    9. Higher-order derivatives
  3. Applications of the Derivative
    1. Graphing functions using the first and second derivatives, concavity, and asymptotes
    2. Maximum and minimum values and optimization
    3. Mean Value Theorem
    4. Newton’s method
  4. Integrals
    1. Antiderivatives and indefinite integrals
    2. Area under a curve
    3. Riemann sums and definite integrals
    4. Properties of the integral
    5. Fundamental Theorem of Calculus
    6. Integrals of inverse functions and transcendental functions such as trigonometric and exponential functions
    7. Integration by substitution
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 the limit of a function, continuity, finding derivatives, solving related rates problems, finding the absolute and relative extrema of functions, and evaluating integrals using Riemannn 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 continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of functions, 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 to promote mathematics discovery and enhance problem solving skills.
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 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 the limit of a function, continuity, finding derivatives, solving related rate problems, finding the absolute and relative extrema of functions,  and evaluating integrals using Riemann sums.
  • Classroom and laboratory discovery activities for content knowledge and conceptual understanding of the topics of calculus.
Sample Assignments:
Outside-of-Class Reading Assignments
  • Read and analyze the text and study lecture notes covering topics such as limits, differentiation, integration and a wide range of applications.
Outside-of-Class Writing Assignments
  • Demonstrate critical thinking skills by analyzing and solving problems using the concepts, techniques and symbols of differential calculus.
Other Outside-of-Class Assignments
  • Problem sets that require students to sketch the graph of functions using the first and second derivatives. 
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:
  • Stewart,James. Single Variable Calculus:Early Transcendentals. 8th Brooks/Cole, 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 210 MATH 900S=MAT-1A+MAT-1B
Board of Trustees Approval Date: 11/13/2018
COR Rev Date: 11/13/2018