Math 218: Differential Calculus

The aim of Math 218 is to prepare students to succeed in calculus. In this scope, the course will focus on, pre-calculus, calculus and academic skills necessary for future success. Students will be introduced to the concepts of differential calculus with special emphasis on their respective applications in the engineering and technology fields.

The content:

Part 1: Real numbers, algebraic expressions, complex numbers, circles, lines. Chap 1 (From Textbook 1) Definition of a function, linear functions and models. Chap 2 (From Textbook 1) Quadratic functions and models, polynomial functions and their graphs, polynomial division, real zeros of polynomials, complex zeros, rational functions. Chap 3 (From Textbook 1)

Part 2: Exponential functions, logarithmic functions, exponential and logarithmic equations, modeling with exponential functions, logarithmic scales. Chap 4 (From Textbook 1)

Part 3: Trigonometric functions and their graphs, inverse trigonometric functions and their graphs, trigonometric identities, addition and subtraction formulas, basic trigonometric equations, polar coordinates and graphs, polar form of complex numbers, de Moivre’s theorem. Chap 5, Chap 6, Chap 7 and Chap 8 (From Textbook 1)

Part 4: Limit and continuity of a functions, derivative of functions.Chap 2 (From Textbook 2) Derivatives of trigonometric functions, derivatives of logarithmic and exponential functions, the chain rule, hyperbolic functions and their derivatives. Chap 3 (From Textbook 2)

Part 5: Maximum and minimum values, the mean value theorem, indeterminate forms and l’Hopital’s rule, summary of curve sketching. Chap 4 (From Textbook 2)

Part 6: Matrices and systems of linear equations, determinants and Cramer’s rule, systems of linear equations, systems of inequalities. Vectors in three dimensions, The dot product, the cross product. Chap 9 and 10 (From Textbook 1)

 

Textbooks:

Textbook 1: Precalculus, Mathematics for CalculusJ. Stewart, L. Redlin and S. WatsonCengage Learning, 7th edition, 2015

Textbook 2: Early TranscendentalsJ. StewartCengage Learning, 8th edition, 2015

Course Learning Outcomes:

• Students will recall the foundational knowledge of algebraic expressions, equations, inequalities and a variety of types of functions (represented verbally, algebraically, graphically, and numerically) to solve problems.
• Students will acquire the knowledge relative to the techniques of differentiation to find the derivatives of various functions and composite functions, apply this knowledge the find maxima and minima, critical points and inflection points.
• Students will appropriately select the technique or formula, set equations and solve problems involving derivatives.
• Students will identify and sketch the graphs of a variety of functions.