(Note: Mods, this is not a maths question per se, so please delete immediately if this is not in line with what is expected here. To all those gearing up to vote down - save it, vote to delete instead.)
I'm planning to buy a few books (Elementary to Intermediate) for the following syllabus. Can you folks recommend a number of books to cover this effectively? I'm not looking for books that will have excessive literature - I'm looking for concice, practice oriented books - something like the Schaum's series.
- Numbers of books should be low
- Books should introductory to intermediate, not very advanced
- Amazon availability would be a huge help
Thanks! The syllabus is below:
1. Solution of Quadratic equations with real coefficients.
2. Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
3. Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
4. Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix, inverse of a square matrix, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations using matrices. Gauss-Jordan Method of Solution of simultaneous linear equations.
5. Linear Algebra: Dependence & independence of vectors, bases and dimensions, spanning, properties of quadratic forms.
7. Two dimensions: Cartesian coordinates, distance between two points, shift of origin. Equation of a straight line in various forms, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines; Equation of a circle, equations of tangent, normal and chord.
8. Differential calculus: Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, exponential and logarithmic functions. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, exponential and logarithmic functions. Derivatives of implicit functions; increasing and decreasing functions, maximum and minimum values of a function; partial derivatives; Lagrange’s Mean Value Theorem; Applications: maxima and minima, optimization.
9. Integral calculus: Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties. Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves, continuous compounding, average value of functions.
10. Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.
11. Numerical Analysis: solution of polynomial & transcendental equations using numerical methods such as Bisection, Newton-Raphson methods, Lagrange’s and Newton’s Interpolating polynomials.