CIC Approval: 11/14/2024
BOT Approval:
State Approval:
Effective Term: Fall 2025

SAN DIEGO COMMUNITY COLLEGE DISTRICT

CITY, MESA, AND MIRAMAR COLLEGES
COURSE OUTLINE

Section I

SUBJECT AREA AND COURSE NUMBER:
Mathematics 121
Basic Techniques of Applied Calculus I
3
Letter Grade or Pass/No Pass
CATALOG COURSE DESCRIPTION:
This course examines the study of calculus using numerical, graphical, and analytical methods to analyze calculus problems encountered in real-world applications in business, natural/life sciences, and social sciences. Topics include limits, derivatives, and integrals of algebraic, exponential, and logarithmic functions, curve sketching, optimization, and areas under and between curves and partial derivatives and optimization of multivariable functions. This is the first course in a sequence of mathematics courses for students intending to major in business, economics, or natural and social sciences.
REQUISITES:
Prerequisite: Successful completion of Intermediate Algebra with a grade of C or better or appropriate placement Milestone M40 or M50 based on California Title 5 regulations. Students with a milestone M30 must enroll in MATH 121X (Mathematics 121 and Mathematics 15F support course).
FIELD TRIP REQUIREMENTS:
May be required
Credit Status
D - Credit - Degree Applicable
Transfer Status
A - Transferable to both UC and CSU.
C-ID:
TOTAL LECTURE HOURS:
48.000 - 54.000
TOTAL LAB HOURS:
0.000 - 0.000
TOTAL OTHER HOURS:
0 - 0
TOTAL CONTACT HOURS:
48 - 54
OUTSIDE-OF-CLASS HOURS:
96.000-108.000
TOTAL STUDENT LEARNING HOURS:
144 - 162
STUDENT LEARNING OBJECTIVES:
Upon successful completion of the course the student will be able to:
Upon successful completion of the course the student will be able to:
  1. Interpret and evaluate limits of algebraic, exponential, and logarithmic functions
  2. Determine the continuity of functions at specific points and in an entire set
  3. Calculate derivatives of algebraic, exponential, and logarithmic functions, applying various rules of derivatives
  4. Analyze and sketch polynomial and rational functions using the first and second derivative
  5. Apply derivatives to solve optimization problems with or without constraints
  6. Apply derivatives of exponential and logarithmic functions to solve business and life science applications
  7. Apply derivatives and integrals to problems relating to business, economics, natural science, and social science
  8. Calculate antiderivatives of functions involving algebraic, exponential, or logarithmic functions
  9. Calculate antiderivatives using the substitution technique
  10. Compute definite integrals by applying the Fundamental Theorem of Calculus, and apply definite integrals to find the area under a curve and between two curves
  11. Calculate derivatives of multivariable functions and apply them to maximization and minimization problems.

Section II

1. COURSE OUTLINE AND SCOPE:
The following topics are included in the framework of the course but are not intended as limits on content. The order of presentation and relative emphasis will vary with each instructor.
Course Lecture Content
  1. Limits and continuity
    1. Intuitive approach to limit
    2. Computational approach to limits
    3. One-sided limits
    4. Limits at infinity
    5. Continuity of functions
    6. Slopes of secant and tangent lines
  2. Derivatives
    1. Rates of change
    2. Definition of the derivative
    3. Techniques for computing derivatives
    4. Derivatives of products and quotients
    5. Chain rule
    6. Implicit differentiation
  3. Curve sketching
    1. Increasing and decreasing functions
    2. Relative and absolute extrema
    3. First derivative test
    4. Concavity and inflection points
    5. Second derivative test
    6. Strategies for graphing
    7. Vertical and horizontal asymptotes
  4. Exponential and logarithmic functions
    1. Algebraic and geometric properties
    2. Applications including growth and decay
    3. Derivatives of exponential and logarithmic functions
  5. Applications of derivatives
    1. Optimization
    2. Related rates
    3. Logarithmic functions
    4. Exponential functions
    5. Practical problems in business, natural science, and social science
  6. Integration
    1. Antiderivative rules
    2. Integration by substitution
    3. Area and the definite integral
    4. Riemann sums
    5. The Fundamental Theorem of Calculus
    6. Rolle's Theorem and Mean Value Theorem
  7. Multivariable calculus
       A.   Functions of several variables
       B.   Partial derivatives
       C.   Maxima and minima
Reading assignments are required and may include, but are not limited to, the following:
  1. Assigned sections in textbook
  2. Related sections in different applied calculus textbooks
  3. Chapters or articles in other mathematics texts or journals, such as The College Math Journal or Mathematics Magazine
  4. Related readings in which calculus techniques are used to address problems in the social and natural sciences
  5. Supplemental online instructional materials, such as MyMathLab, MathXL, WebAssign, or Blackboard.
Writing assignments are required and may include, but are not limited to, the following:
  1. Journal entries that focus on mathematical calculations, problem solving techniques, and applied problems
  2. Essay homework questions that require descriptions in complete sentences and usage proper mathematical terminology, proofs of mathematical statements, procedures for performing complicated computations, or solutions to applied problems
  3. Report on some topic or person appropriate to mathematics
  4. Proofs of mathematical statements related to the material covered in class
Outside assignments may include, but are not limited to, the following:
  1. Using spreadsheet programs, such as Microsoft Excel, and Computer Algebraic Systems (CAS) packages, such as Maple, Derive, MathCad, MPP, or Mathematica
  2. Reading and writing assignments as specified in the course syllabus
  3. Reading and reviewing lecture notes
  4. Viewing assigned/recommended media materials
  5. Attending field trips to pertinent lectures/conferences
  6. Completing an analytical semester project based on a logistic growth function or maximizing profit or constuctions costs
  7. Developing problem solving techniques and analytical skills by solving problems from various texts, such as the Calculus Problem Solver or Schaums Calculus Outline
  8. Preparing collaborative projects focusing on expanding mathematical concepts presented in class.
Critical thinking assignments are required and may include, but are not limited to, the following:
  1. Apply algebraic, numeric, and geometric techniques to analyze problems
  2. Create appropriate functions to model dynamic and static phenomena
  3. Apply appropriate calculus principles to solve a variety of optimization problems
  4. Interpret and analyze calculus principles, symbolic formulas, and problem solving techniques
  5. Analyze and solve problems involving derivatives or antiderivative introduced in the text
  6. Develop proofs for mathematical statements
2. METHODS OF EVALUATION:
A student's grade will be based on multiple measures of performance unless the course requires no grade. Multiple measures may include, but are not limited to, the following:

  • Other: In-class objective quizzes and/or examinations Comprehensive final examination Out-of-class writing assignments that develop critical thinking and problem solving techniques Exploratory activities involving a graphing calculator or computer Class participation Oral presentations Group projects
3. METHODS OF INSTRUCTION:
Methods of instruction may include, but are not limited to, the following:

  • Lecture
  • Lecture Discussion
  • Audio-Visual
  • Collaborative Learning
  • Distance Education (Fully Online)
  • Distance Education (Partially Online)
4. REQUIRED TEXTS AND SUPPLIES:
Textbooks may include, but are not limited to:
  1. Barnett, Raymond, et al, Finite Mathematics for Business, Economics, Life Sciences and Social Sciences, 14th, Pearson, 2018, ISBN:9780134675985
  2. Hoffman, Laurence, et al, Applied Calculus: For Business, Economics, and the Social and Life Sciences, Expanded Edition, 11th, McGraw-Hill, 2012, ISBN:978007353237
  3. Berresford, Geoffrey, and Andrew Rockett, Applied Calculus, 7th, Cengage, 2015, ISBN:978130508531
  4. Larson, Ron, Calculus: An Applied Approach, 10th , Cengage, 2016, ISBN:9781305860926
  5. Tan, S.T, Applied Calculus for the Managerial, Life, and Social Sciences, 10th, Cengage, 2014, ISBN:9781285464640
  1. Graphing calculator
  2. Graph paper
5. ORIGINATION DATA
Lan Hong
05/06/2024