# Engineering Mathematics – Calculus

## Engineering Mathematics – Calculus ePrep course

Textbook Features of Calculus by Stewart, 9th Edition

• USEFUL EXAMPLES: Every concept is presented with examples that show clear working steps so as to stimulate students to inculcate the viewing of the subject analytically. Many detailed examples display well worked solutions pictorially, analytically, and/or numerically to enable better understanding of the subject. Additional notes on the solution steps further help to provide greater understanding of the solution approach.
• NEW EXPLANATIONS AND EXAMPLES: Careful refinements throughout provide even greater clarity on key concepts such as computing volumes of revolution, and applying triple integrals.
• FOCUSSED PROBLEM-SOLVING:  Problem-solving utilizing George Polya’s methodology is implemented. “Strategies” sections help students select which of the techniques they can apply to solve problems when the choice is not obvious and help them enhance true problem-solving skills and intuition.
• PREREQUISITE SUPPORT: To facilitate learning of calculus, the students first perform diagnostic tests to gauge their proficiencies in prerequisites including algebra, analytic geometry, functions, and trigonometry, and to  enable students to improve their competencies in these prerequisites.
• STEM APPLICATIONS: The applications of Calculus as a problem-solving tool in sciences, engineering, medicine, and the social sciences are well illustrated by the authors through “When will I use this?”
• STIMULATING PROJECTS: There are various categories of stimulating projects for students to enhance their comprehension of calculus concepts. There is the “Writing Projects” comparing present-day methods with those of the early-day  methods of calculus. There is the “Discovery Projects” for students to discover the knowledge on their own. There is the “Applied Projects”  that enable students to learn the real-world application of mathematics, especially calculus. “Laboratory Projects” anticipate results to be discussed later or encourage discovery through pattern recognition.
• EXCELLENT PROGRESSIVE EXERCISES: There are more than 8000 exercises in total, and the exercises are set such that they progress from skill-development problems to more challenging problems involving applications and proofs. Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. More challenging “Problems Plus” exercises reinforce concepts by requiring students to apply techniques from more than one chapter of the text, and by patiently showing them how to approach a challenging problem.
• CLEAR EXPOSITION: Dan Clegg and Saleem Watson have remained true to James Stewart’s writing style speaking clearly and directly to students, guiding them through key ideas, theorems and problem-solving steps, and encouraging them to think as they read and learn calculus.
• SUBHEADINGS OF CONTENTS: Additional subsections within chapters help instructors and students find key content more easily to make the text an even more helpful teaching and learning tool.
• NEW SCAFFOLDED EXERCISES: At the beginning of problem sets, new basic exercises reinforce key skills and build student confidence to prepare them for more rigorous exercises and conceptual understanding.

## Engineering Mathematics – Calculus ePrep course

Textbook Contents of Calculus by Stewart, 9th Edition.

The Chapter Headings are given below, and details are provided in Calculus Contents

Diagnostic Tests

A Preview of Calculus

1 Functions and Limits

2 Derivatives

3 Applications of Differentiation

4 Integrals

5 Applications of integration

6 Inverse Functions:  Exponential, Logarithmic, and Inverse Trigonometric Functions

7 Techniques of Integration

8 Further Applications of Integration

9 Differential Equations

10 Parametric Equations and Polar Coordinates

11 Infinite Sequences and Series

12 Vectors and the Geometry of Space

13 Vector Functions

14 Partial Derivatives

15 Multiple Integrals

16 Vector Calculus

17 Second-Order Differential Equations