Each session I would come in with a new topic that had just been assigned and I had no clue how to do it. Nathan is a smart, kind, and helpful tutor more math topics. Joshua, 20 lessons with Nathan Kind and Helpful tutor that knows his subject. I would not hesitate to recommend Nathan to friends and family so if you’re looking for a tutor he is a great choice. The way he solves problems is very thorough to the point where I can go back to our old work and remember every step we did. He is also very patient when explaining and was very flexible with his schedule. Nathan does a really excellent job laying out helpful formulas and notes to help solve complex problems. We solved problems together instead of him just explaining everything so that I really understood the material. He was knowledgeable about every topic we talked about and patient with his explanations. Adequate references to the previously appeared results are made in the text and unnecessary repetitions are avoided.Increased test scores by average of 20 points in less than 3 weeks When the number c coincides with the chapter at hand it is dropped. For instance, the equation number (c.s.e) refers to the eth equation in the sth section of Chapter c. These subtitles within the Sections are numbered in decimal pattern. The discussion within the Sections is presented in the form of Definitions, Theorems, Corollaries, Notes and (solved) Examples. Chapters are divided into Sections, which are numbered chapter-wise. The alphabetical index added at the end makes the access to the contents faster. Tutorial sheets and Test Papers containing model questions and a short bibliography of the topics are provided. Besides several worked out exercises (called Examples), Chapters 5, 7 and 8 are also supplemented by Problem-sets of unsolved exercises with necessary hints to the challenging ones. The total derivative of functions and famous Euler’s theorem on homogeneous functions are explained. Both vector and scalar functions are considered and the vector differential operator of the first order is introduced. The last chapter deals with the partial derivation of functions of more than one variable. Applications of vectors to geometry dealing with the vector equations of straight lines and planes are given in the Chapter 7. Two Eulerian integrals, usually called Beta and Gamma functions, are also introduced and some properties of Gamma functions are given. Power series, Maclaurin’s and Taylor’s expansions are explained in detail in the same chapter. Presuming that the students already had a first course on calculus only main concepts and results of differentiation and integration of functions of single variable have been given in the chapter 6. A comprehensive course on convergence of infinite series forms the subject mater of Chapter 5. Further concepts such as rank of a matrix etc. Matrix algebra including multiplication of matrices is given. The next chapter deals with the matrices and determinants. Vector algebra and products of vectors are included. Vectors (mostly in 3-dimensional space) are introduced in the third chapter. A brief discussion of theory of equations is given in the second chapter. The first chapter deals with the introductory topics in 2-dimensional coordinate geometry: straight lines and conic sections. The book, having eight chapters, offers one semester course (with four credit hours per week) on diverse topics usually included in the mathematics syllabus of the first year Engineering class of most Universities.
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