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This is a textbook on basic to intermediate mathematics for undergraduate students majoring in the physical sciences and engineering. Many chapters, covering topics like Green's functions, calculus of variations, and functions of a complex variable, are well-suited for graduate classes. Additionally, researchers can benefit from the book as a mathematical refresher for their professional work. The book provides readers with a fundamental understanding of underlying principles, using derivations based more on mathematical intuition rather than exposing them to multiple theorems, proofs, and lemmas. Each chapter includes highly relevant examples with detailed solutions and explanations, promoting a practical application of knowledge to real problems in the physical sciences. For the convenience of both students and instructors, there are end-of-chapter exercises with answers that can be easily utilized for assignments. The book is not a replacement for calculus textbooks, but rather a guide to the mathematics most relevant to the physical sciences and engineering. In conclusion, this book can be readily adapted for upper-level undergraduate and graduate classes, particularly those focusing on mathematical methods for students in physical sciences, applied mathematics, and engineering majors