The following sections will be presented:

• Sets of Numbers: Principle of Mathematical Induction.
• Functions: Definition of a Function, Notation, Basic Functions, Calculus of Functions, Alternative Definition of a Function.
• Graphs: Intervals, Distance Between Points, Graph of a Function, Linear Function, Power Functions – Rational Functions, Even and Odd Functions, Relationships Between Graphs, One-to-One and Onto Functions – Inverse Function.
• Limits: The Limit Intuitively, Definition of Limit of a Function, Geometric Interpretation of Limit, Properties of Limit, One-Sided Limits, Limits at Infinity.
• Continuous Functions: Definition of Continuity of Functions, Calculus of Continuous Functions, Continuity of Composite Functions, Continuity and Sign Preservation.
• Suprema and Infima: Definition of Supremum, Definition of Infimum, Properties.
• Continuity and Applications: Bolzano Theorem, Bounded Function Theorem, Maximum and Minimum Value Theorem, Intermediate Value Theorem (IVT).
• Derivatives: Ratio of Change, Rate of Change, Derivative Function, Derivative Vs Continuity.
• Differentiation: Simple Rules of Differentiation, Derivative of Sum of Functions, Derivative of Product of Functions, Derivative of Product of a Function with a Scalar, Derivative of a Power – Polynomial, Derivative of Quotient of Functions, Derivative of Composition of Functions.
• Usage of Derivative: Extrema of a Function, Fermat’s Theorem, Local Extrema of a Function, Finding Extrema of a Function in a Closed Space, Rolle’s Theorem, Mean Value Theorem (MVT), Monotonicity of a Function, Finding Local Extrema, Graphing a Function, Cauchy’s Mean Value Theorem (CMVT), L’ Hôpital’s Rule.
• Curvature: Convex Functions, Concave Functions, Characterization of Convex Functions, Curvature and Differentiation.
• Integrals: Partition of an Interval, Upper and Lower Sum of a Function with respect to a Partition, Definition of Integral, Integral as Area Under a Curve, Integral Properties, Mean Value Theorem of Integral Calculus (MVTIC), Riemann Sum, Fundamental Theorem of Calculus.
• Logarithmic and Exponential Function: Powers, Logarithmic Function, Properties of Logarithmic Function, Exponential Function, Properties of Exponential Function, Power Function.
• Elementary Methods of Integration: Indefinite and Definite Integrals, Basic Indefinite Integrals, Properties of Indefinite Integrals, Integration by Parts, Substitution Rule.
• Infinite Sequences: Sequences of Real Numbers, Convergence of Sequences, Properties of Sequences, Monotonicity and Bounds of Sequences, Convergence Criterion of Sequences, Limits as Upper or Lower Sums of Functions.
• Infinite Series: Series of Real Numbers, Properties of Series, Zero Convergence Condition, Geometric Series, Exponential Series, Boundedness Criterion, Comparison Criterion, Ratio Criterion, Integral Criterion.