Pure Mathematics 2; A Second Course

Specifications

Book Description

“Pure Mathematics 2: A Second Course” by J.K. Backhouse, S.P.T. Houldsworth, and B.E.D Cooper is a continuation of the exploration of pure mathematics, building upon the foundational concepts introduced in the first course. Here's an overview of what you can expect from this book:

1. Advanced Algebra: The book delves deeper into algebraic concepts, covering topics such as quadratic equations, inequalities, functions, and graphs. It explores advanced techniques for solving equations and manipulating functions, including polynomial and rational functions.
2. Trigonometry: Trigonometric functions and identities are studied in greater detail, including trigonometric equations, properties of trigonometric functions, and applications of trigonometry in geometry and physics. The book may also cover topics such as inverse trigonometric functions and the complex representation of trigonometric functions.
3. Coordinate Geometry: The text extends the study of coordinate geometry to higher dimensions, exploring topics such as vectors, vector equations of lines and planes, and vector calculus. It covers applications of vectors in geometry, physics, and engineering, as well as techniques for solving problems involving vectors.
4. Calculus: Building upon the calculus concepts introduced in the first course, this book explores more advanced topics in differential and integral calculus. It covers techniques for differentiation and integration, including applications of calculus in optimization, related rates, and curve sketching.
5. Sequences and Series: The book extends the study of sequences and series to more advanced topics, such as power series, Taylor series, and convergence tests for series. It explores applications of series in calculus, differential equations, and mathematical analysis.
6. Complex Numbers: Complex analysis is introduced, covering topics such as complex functions, differentiation of complex functions, and contour integration. The book may also cover applications of complex analysis in physics, engineering, and other fields.
7. Further Topics: Depending on the edition, the book may include additional topics such as discrete mathematics, number theory, and group theory. These topics provide further depth and breadth to the study of pure mathematics and may serve as a bridge to more advanced courses in mathematics and related disciplines.
8. Exercises and Examples: Like the first course, the book includes numerous exercises and worked examples to reinforce learning and develop problem-solving skills. These exercises range from basic drills to more challenging problems, allowing students to practice and apply their understanding of advanced mathematical concepts.

Overall, “Pure Mathematics 2: A Second Course” serves as a comprehensive resource for students studying advanced pure mathematics at the undergraduate level. It provides a rigorous treatment of mathematical concepts and techniques, preparing students for further study and research in mathematics and related fields.