Mathematics: Calculus I-

Limits- One-Sided Limits, Limits at a Point, Limits at Infinity, Infinite Limits, Limits of Sequences, Limits Involving Piecewise Functions, Composite Limits.

Differentiation- Applications of Differentiation, Derivative, Partial Differentiation, Implicit Differentiation, Higher-Order Differentiation, Vector Differentiation, Functional Differentiation, Total Differentiation, Parametric Differentiation, Numerical Differentiation, Automatic Differentiation.

Integration- Applications of Integration, Indefinite Integration, Definite Integration, Integration by Substitution (U-Substitution), Integration by Parts, Partial Fraction Decomposition, Trigonometric Integrals, Integration of Exponential and Logarithmic Functions, Improper Integrals.

The Fundamental Theorem of Calculus- First Fundamental Theorem of Calculus, Second Fundamental Theorem of Calculus.

Sequences and Series- Sequences:– Arithmetic Sequence, Geometric Sequence, Fibonacci Sequence, Harmonic Sequence, Square Numbers Sequence.

Series: Arithmetic Series, Geometric Series, Convergent Series, Divergent Series, Alternating Series, Power Series.

Multivariable Calculus (Possibly)- Partial Derivatives, Gradient, Divergence, Curl, Line Integrals, Surface Integrals, Vector Fields, Scalar Fields, Double and Triple Integrals, Change of Variables, Vector Calculus Theorems.