What textbooks should I use for Trigonometry and Calculus? My basics are terrible.

manpreet Best Answer 2 years ago

I need help really bad. I have a paper coming up in two months and all topics require at least basic if not intermediate understanding in trigonometry and calculus. I don't know how I got so far - by memorizing formulas just before an exam. I like mathematics but I am terrible at learning these identities.

I have one paper coming up and need a lot of practice. These are the topics that is going to be covered in the paper:

Differential calculus:

Definition of the limit of a function in ε-δ form- Algebra of limits-Continuity of a function - types of discontinuities -properties of continuous functions on a closed interval (boundedness, attainment of bounds and taking every value between bounds) - differentiability, differentiability implies continuity and converse is not true. Rolle’s theorem-Lagrange’s and Cauchy’s first mean value theorems - Taylors’ theorem with Lagrange’s form of remainder - Maclaurin’s expansion- problems. Evaluation of limits by L’Hospital’s rule (indeterminate form).

Group Theory:

Recapitulation of the definition and standard properties of groups and subgroups Cyclic groups- properties-order of an element of a group- properties related to order of an elementsubgroup generated by an element of a group- coset decomposition of a group- modulus relation- index of a group- Lagrange's theorem for finite groups-consequences.

Sequences:

Definition of a sequence-limit of a sequence-algebre of limits. Convergent, divergent and oscillatory sequence-infimum-supremum-Nature of the sequences theorems-problems-monotonicity-problems-cauchy sequences.

Series:

Definition of Convergence-divergence-oscillation-properties of convergent series- Cauchy’s theorem-geometric series - p-series -comparison tests, De'alembert's test, Raabe's tests. Cauchy root test - problems. (The following tests are without proof) Absolute-conditional convergence-De'alembert's test for absolute convergence Alternating series. Summation of series - binomial, exponential and logarithmic series.

Differential Equations:

i. Formation and solution of ordinary differential equations (I order & I degree). a) Variable-separable and reducible to variable separable form b) Homogeneous & reducible to homogeneous forms c) Linear equations- Bernoulli’s equations and those reducible to these equations d) Exact equations and reducible to exact with standard integrating factors ii. Equation of first order and higher degree-Clairaut’s equation -general and singular solutions- geometric meaning. iii. Orthogonal trajectories in cartesian and polar forms.

How should I go about learning the basics for these topics in order to understand the syllabus better?

Thank you so much.

manpreet 2 years ago