Renowned applied mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and Kalman filtering and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians. The only prerequisite is a basic course in linear algebra.
William Gilbert Strang (born November 27, 1934), usually known as simply Gilbert Strang or Gil Strang, is an American mathematician, with contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra. He has made many contributions to mathematics education, including publishing seven mathematics textbooks and one monograph. Strang is the MathWorks Professor of Mathematics at the Massachusetts Institute of Technology. He teaches Introduction to Linear Algebra and Computational Science and Engineering and his lectures are freely available through MIT OpenCourseWare.
There are many techniques involved. This is a textbook that is more about if you know the material or not. There are parts in here that are vague that do incline you to do your own research, or have prior knowledge, in order to understand particular topics.
Strang's book consists a wide range of mathematics from the fields of engineering and physics that is all over the place. If you have a really good grasp on math in different fields, you will have no trouble in understanding these fundamentals.