Course Outline for Mathematics 16
Applied Calculus II

Effective: Fall 2022
SLO Rev: 10/26/2021
Catalog Description:

MTH 16 - Applied Calculus II

3.00 Units

Techniques of integration; multivariable calculus; calculus of trigonometric functions; differential equations; Taylor polynomials. Applications in business, economics and the life and social sciences. Integration includes by parts, using tables, and improper integrals. Multivariable calculus topics include partial derivatives and finding local extrema. Differential Equations includes separable equations. Applications include probability distributions.
Prerequisite: MTH 15 or an appropriate skill level demonstrated through the Mathematics Assessment process. Strongly Recommended: MTH 22 or MTH 36 or MTH 37.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 0.00 18.00 0.00 18.00
Total 3.00 72.00 108.00 180.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. find antiderivatives using integration by parts and tables of integrals;
  2. evaluate improper integrals;
  3. find partial derivatives;
  4. solve optimization and constrained optimization problems involving functions of two variables;
  5. evaluate double integrals;
  6. find derivatives and integrals of trigonometric functions;
  7. solve applied problems involving differentiation or integration of trigonometric functions;
  8. solve simple differential equations;
  9. solve problems involving exponential growth/decay, limited growth, and logistic growth;
  10. approximate functions with Taylor Polynomials;
  11. find event probabilities by integrating probability density functions;
  12. find expected value, variance, and standard deviation of continuous random variables;
  13. solve applications of integration in Business and Economics.
Course Content:
  1. Integration Techniques
    1. Integration by parts
    2. Integration using tables
    3. Applications
    4. Improper integrals
  2. Multivariable Calculus
    1. Functions of several variables
    2. Partial derivatives
    3. Gradient
    4. Maxima and minima
    5. Lagrange multiplier
    6. Optimization and constrained optimization
    7. Double integrals
    8. Applications
  3. Trigonometric Functions
    1. The unit circle
    2. Definitions of trigonometric functions
    3. Derivatives of trigonometric functions
    4. Integrals of trigonometric functions
    5. Applications
  4. Differential Equations
    1. Solutions of differential equations
    2. Separation of variables
    3. Euler's method
    4. Applications
      1. Population models
      2. Logistic growth
  5. Taylor Polynomials
    1. Definition
    2. Interval of convergence
    3. Error bound
  6. Probability and Calculus
    1. Continuous probability model
    2. Expected value and variance
Methods of Instruction:
  1. Lecture/Discussion
  2. Group Activities
  3. Distance Education
  4. Problem Solving
Assignments and Methods of Evaluating Student Progress:
  1. The concentration (in mg/mL) of a certain drug in a patient’s bloodstream t hours after it has been administered is given by the absorption model. Find the average concentration of the drug in the patient’s bloodstream over the first 12 hours after administration.
  2. A company produces two types of desks, x finished desks and y unfinished desks per week. The total weekly profit (in dollars) is given by the profit function. If the company’s management decides to restrict the production of these desks to a total of 200 desks per week, how many finished desks and how many unfinished desks should be produced each week to maximize the company’s weekly profit?
  3. The life span of a certain plant species (in days) is described by the probability density function. Find the probability that a plant of this species will live for 100 days or less.
  4. The weekly closing price (in dollars per share) of XYZ Corporation stock in week t is approximated by price function. Find the average closing price of the stock over the 15-week period.
  1. Exams/Tests
  2. Quizzes
  3. Home Work
  4. Final Examination
  5. Class Work
Upon the completion of this course, the student should be able to:
  1. critically analyze mathematical problems using a logical methodology;
  2. communicate mathematical ideas, understand definitions, and interpret concepts;
  3. increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Barnett, Z. (2019). Calculus for Business, Economics, Life Sciences, and Social Sciences (14th). Pearson.
  • Scientific or graphing calculator
Abbreviated Class Schedule Description:
Techniques of integration; multivariable calculus; calculus of trigonometric functions; differential equations; Taylor polynomials. Applications in business, economics and the life and social sciences.
Prerequisite: MTH 15 or an appropriate skill level demonstrated through the Mathematics Assessment process. Strongly Recommended: MTH 22 or MTH 36 or MTH 37.
Discipline:
Mathematics*