What do you learn in calculus?

Algebra (Math 1314) - Topics included in this set of notes :

• Preliminaries - Exponent Properties, Rational Exponents, Negative Exponents, Radicals, Polynomials, Factoring, Rational Expressions, Complex Numbers
• Solving Equations and Inequalities - Linear Equations, Quadratic Equations, Completing the Square, Quadratic Formula, Applications of Linear and Quadratic Equations, Reducible to Quadratic Form, Equations with Radicals, Linear Inequalities, Polynomial & Rational Inequalities, Absolute Value Equations & Inequalities.
• Graphing and Functions - Graphing Lines, Circles, and Piecewise Functions, Function Definition, Function Notation, Function Composition, Inverse Functions.
• Common Graphs - Parabolas, Ellipses, Hyperbolas, Absolute Value, Square Root, Constant Function, Rational Functions, Shifts, Reflections, Symmetry.
• Polynomial Functions - Dividing Polynomials, Zeroes/Roots of Polynomials, Finding Zeroes of Polynomials, Graphing Polynomials, Partial Fractions.
• Exponential and Logarithm Functions - Exponential Functions, Logarithm Functions, Solving Exponential Functions, Solving Logarithm Functions, Applications.
• Systems of Equations - Substitution Method, Elimination Method, Augmented Matrix, Nonlinear Systems.

The Algebra notes/tutorial assume that you've had some exposure to the basics of Algebra. In particular it is assumed that the exponents and factoring sections will be more of a review for you. Also, it is assumed that you've seen the basics of graphing equations. Graphing particular types of equations is covered extensively in the notes, however, it is assume that you understand the basic coordinate system and how to plot points.

Calculus I (Math 2413) - Topics included in this set of notes are :

• Algebra/Trig Review - Trig Functions and Equations, Exponential Functions and Equations, Logarithm Functions and Equations.
• Limits - Concepts, Definition, Computing, One-Sided Limits, Continuity, Limits Involving Infinity, L'Hospitals Rule
• Derivatives - Definition, Interpretations, Derivative Formulas, Power Rule, Product Rule, Quotient Rule, Chain Rule, Higher Order Derivatives, Implicit Differentiation, Logarithmic Differentiation, Derivatives of Trig Functions, Exponential Functions, Logarithm Functions, Inverse Trig Functions, and Hyperbolic Trig Functions.
• Applications of Derivatives - Related Rates, Critical Points, Minimum and Maximum Values, Increasing/Decreasing Functions, Inflection Points, Concavity, Optimization
• Integration - Definition, Indefinite Integrals, Definite Integrals, Substitution Rule, Evaluating Definite Integrals, Fundamental Theorem of Calculus
• Applications of Integrals - Average Function Value, Area Between Curves, Solids of Revolution, Work.

The Calculus I notes/tutorial assume that you've got a working knowledge of Algebra and Trig. There is some review of a couple of Algebra and Trig topics, but for the most part it is assumed that you do have a decent background in Algebra and Trig. These notes assume no prior knowledge of Calculus.

Calculus II (Math 2414) - Topics included in this set of notes are :

• Integration Techniques - Integration by Parts, Integrals Involving Trig Functions, Trig Substitutions, Integration using Partial Fractions, Integrals Involving Roots, Integrals Involving Quadratics, Integration Strategy, Improper Integrals, Comparison Test for Improper Integrals, and Approximating Definite Integrals.
• Applications of Integrals - Arc Length, Surface Area, Center of Mass/Centroid, Hydrostatic Pressure and Force, Probability.
• Parametric Equations and Polar Coordinates - Parametric Equations & Curves, Calculus with Parametric Equations (Tangents, Areas, Arc Length and Surface Area), Polar Coordinates, Calculus with Polar Coordinates (Tangents, Areas, Arc Length and Surface Area).
• Sequences and Series - Sequences, Series, Convergence/Divergence of Series, Absolute Series, Integral Test, Comparison Test, Limit Comparison Test, Alternating Series Test, Ratio Test, Root Test, Estimating the Value of a Series, Power Series, Taylor Series, Binomial Series
• Vectors - Basics, Magnitude, Unit Vector, Arithmetic, Dot Product, Cross Product, Projection
• Three Dimensional Coordinate System - Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates

The Calculus II notes/tutorial assume that you've got a working knowledge Calculus I, including Limits, Derivatives, and Integration (up to basic substitution). It is also assumed that you have a fairly good knowledge of Trig. Several topics rely heavily on trig and knowledge of trig functions.

Calculus III (Math 3435) - Topics included in this set of notes are :

• Three Dimensional Coordinate System - Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates
• Partial Derivatives - Limits, Partial Derivatives, Higher Order Partial Derivatives, Differentials, Chain Rule, Directional Derivatives, Gradient.
• Applications of Partial Derivatives - Tangent Plane, Normal Line, Relative Extrema, Absolute Extrema, Optimization, Lagrange Multipliers.
• Multiple Integrals - Iterated Integrals, Double Integrals, Double Integrals in Polar Coordinates, Triple Integrals, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Change of Variables, Surface Area.
• Line Integrals - Vector Fields, Line Integrals With Respect to Arc Length, Line Integrals With Respect to x and y, Line Integrals of Vector Fields, Fundamental Theorem of Line Integrals, Conservative Vector Fields, Potential Functions, Green's Theorem, Curl, Divergence.
• Surface Integrals - Parametric Surfaces, Surface Integrals, Surface Integrals of Vector Fields, Stokes' Theorem, Divergence Theorem.

The Calculus III notes/tutorial assume that you've got a working knowledge Calculus I, including limits, derivatives and integration. It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space.

Differential Equations (Math 3301) - Topics included in this set of notes are :

• First Order Differential Equations - Linear Equations, Separable Equations, Exact Equations, Equilibrium Solutions, Modeling Problems.
• Second Order Differential Equations - Homogeneous and Nonhomogeneous Second Order Differential Equations, Fundamental Set of Solutions, Undetermined Coefficients, Variation of Parameters, Mechanical Vibrations
• Laplace Transforms - Definition, Inverse Transforms, Step Functions, Heaviside Functions, Dirac-Delta Function, Solving IVP's, Nonhomogeneous IVP, Nonconstant Coefficient IVP, Convolution Integral.
• Systems of Differential Equations - Matrix Form, Eigenvalues/Eigenvectors, Phase Plane, Nonhomogeneous Systems, Laplace Transforms.
• Series Solutions - Series Solutions, Euler Differential Equations.
• Higher Order Differential Equations - n^th order differential equations, Undetermined Coefficients, Variation of Parameters, 3 x 3 Systems of Differential Equations.
• Boundary Value Problems & Fourier Series - Boundary Value Problems, Eigenvalues and Eigenfunctions, Orthogonal Functions, Fourier Sine Series, Fourier Cosine Series, Fourier Series.
• Parital Differential Equations - Heat Equation, Wave Equation, Laplace's Equation, Separation of Variables.

These notes assume no prior knowledge of differential equations. A good grasp of Calculus is required however. This includes a working knowledge of differentiation and integration.