# Syllabus ENGR 190 Introductory Calculus (QR)

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1 Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S. and M. Eng. Degrees. Review of algebra, trigonometry, analytic geometry, and introduction of elementary calculus in preparation for Engineering Analysis I. Textbook: Precalculus: A Right Triangle Approach 1/e by Kirk Trigsted and supplemental introductory calculus material Instructor: James E. Lewis, Ph.D., JS 117 (502) Brian S. Robinson, Ph.D., JS 113 (502) Chris Foreman, Ph.D., Vogt 305 (502) Objectives: This course is designed to give students a solid background in algebra, trigonometry, analytic geometry, and an introduction to differential calculus while developing their ability to think critically as they solve problems and work collaboratively with their peers. Topics: 1. Order of Operations, The Laws of Exponents; Radicals, Polynomials, Factoring Polynomials, Rational Expressions (6 hours) 2. Linear Equations, Systems of Linear Equations in Two Variables, Applications of Linear Equations, Complex Numbers, Quadratic Equations, Applications of Quadratic Equations, Other Types of Equations, Linear Inequalities, Absolute Value Equations and Inequalities, Polynomial and Rational Inequalities (7 hours) 3. The Rectangular Coordinate System, Circles, Lines, Parallel and Perpendicular Lines (6 hours) 4. Properties of a Function's Graph, Graphs of Basic Functions; Piecewise Functions, Transformations of Functions, The Algebra of Functions; Composite Functions, One-to-One Functions; Inverse Functions, Quadratic Functions, Applications and Modeling of Quadratic Functions, The Graphs of Polynomial Functions (6 hours) 5. The Factor Theorem, Zeros of Polynomial Functions; Fundamental Theorem of Algebra, Rational Functions and Their Graphs, horizontal, vertical, and oblique (slant) asymptotes, solving problems that involve variation (6 hours) 6. Exponential Functions, The Natural Exponential Function, Logarithmic Functions, Properties of Logarithms, Exponential and Logarithmic Equations, Applications of Exponential and Logarithmic Functions (6 hours) 7. Degree and Radian Measure, Applications of Radian Measure, Triangles, Right

2 Triangle Trigonometry, Trigonometric Functions of General Angles, The Unit Circle, The Graphs of Sine, Cosine Tangent, Cosecant, Secant, and Cotangent Functions, Phase Shift of Trigonometric functions, Trigonometric Identities, The Sum and Difference Formulas, The Double-Angle and Half -Angle Formulas, The Product-to-Sum and Sum-to-Product Formulas, Trigonometric Equations (7 hours) 8. Geometric and algebraic representations of vectors, operations on vectors, direction and magnitude and direction of a vector, understanding the dot product and its properties, solving applications involving force and work (6 hours) 9. Finding limits using graphs, one-sided limits, properties of limits, average rate of change, instantaneous rates of change and introduction to derivatives (6 hours) Evaluation: Exams 60%, Quizzes 5%, Final Examination - 20%, Group Exercises 15% Grading Scale (%): A 90> B 80>C 70>D 60>F a minimum score of 70% on the final exam is required to earn a passing grade. General Education (Cardinal Core) Learning Outcomes and Assessment: (for all sections of this course) 1) Interpret information presented in mathematical and/or statistical forms. How course meets outcome: Students are required to set up and solve problems using appropriate algebraic, trigonometric, geometric, or calculus symbols, graphs, and numbers which will require student interpretation of the information to then present in mathematical form. 2) Illustrate and communicate mathematical and/or statistical information symbolically, visually, and/or numerically. How course meets outcome: Students are required to set up and solve problems using appropriate algebraic, trigonometric, geometric, or calculus symbols, graphs, and numbers which will require illustrations and symbolic and/or numerical communication. 3) Determine when computations are needed and execute the appropriate computations. How course meets outcome: Students are required to set up and solve problems using appropriate algebraic, trigonometric, geometric, or calculus symbols, graphs, and numbers which will require students to execute appropriate needed computations. 4) Apply an appropriate model to the problem to be solved.

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