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Oscar E. Fernandez
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Courses
Calculus 1 (Math 115)
Lesson 1: A Brief Review of Algebra and Geometry
Lesson 2: A Review of the Basics of Functions
Lesson 3: A Review of Non-Linear Algebraic Functions
Lesson 4: One-Sided Limits
Lesson 5: Two-Sided Limits; Continuity
Lesson 6: Computational Techniques for Evaluating Limits
Lesson 7: Limits Involving Infinity
Lesson 8: Instantaneous Speed and the Derivative at a Point
Lesson 9: The Derivative Function
Lesson 10: Differentiation Rules I
Lesson 11: Differentiation Rules, Part 2; Higher-Order Derivatives
Lesson 12: Related Rates
Lesson 13: Linearization; Increasing/Decreasing Test
Lesson 14: Optimization Theory
Lesson 15: Applications of Optimization
Lesson 16: The Second Derivative, Revisited; Distance as Area
Lesson 17: The Fundamental Theorem of Calculus
Lesson 18: Integration Properties and Rules
Lesson 19: The Substitution Technique; Applications of Integration
Lesson 20: Exponential and Logarithmic Functions
Lesson 21: Review of Trigonometry
Lesson 22: Trigonometric Functions
Lesson 23: Limits of Transcendental Functions
Lesson 24: Derivatives of Transcendental Functions
Lesson 25: Applications of Derivatives of Transcendental Functions
Lesson 26: Optimization Theory of Transcendental Functions
Lesson 27: Integrals of Transcendental Functions
Calculus 2 (Math 116)
Lesson 1: Review of Precalculus
Lesson 2: Review of Limits, Differentiation
Lesson 3: Introduction to Sequences
Lesson 4: Convergence of Sequences
Lesson 5: Series
Lesson 6: Special Series; the Series Laws
Lesson 7: The Limit and Direct Comparison Tests
Lesson 8: Alternating Series; Absolute and Conditional Convergence
Lesson 9: L'Hopital's Rule
Lesson 10: The Ratio Test
Lesson 11: Power Series
Lesson 12: Power Series as Functions
Lesson 13: Taylor Polynomials
Lesson 14: Taylor’s Theorem
Lesson 15: Taylor Series
Lesson 16: Applications of Taylor Series
Lesson 17: Areas, and Approximating Them via Riemann Sums
Lesson 18: Numerical Integration
Lesson 19: Review of Calculus 1 Integration
Lesson 20: Integration Techniques: u-Substitution
Lesson 21: Integration Techniques: Integration by Parts
Lesson 22: Integration Techniques: Trigonometric Integrals
Lesson 23: Integration Techniques: Trigonometric Substitution
Lesson 24: Integration Techniques: Partial Fractions
Lesson 25: Improper Integrals
Lesson 26: Applications of Series to Integration, and Vice Versa
Lesson 27: Applications of Integration: Area Between Curves
Lesson 28: Applications of Integration: Volumes: Cross-Sections
Lesson 29: Applications of Integration: Volumes of Revolution
Lesson 30: Applications of Integration: The Shell Method
Lesson 31: Applications of Integration: Arc Length
Lesson 32: Applications of Integration: Surface Area
Lesson 33: Capstone: Calculus II
Calculus 3 (Multivariable) (Math 205)
Unit 1: Vectors and Euclidean Spaces
Lesson 0: Introduction to Multivariable Calculus
Lesson 1: 3D Coordinate Systems
Lesson 2: Vectors; The Dot Product
Lesson 3: The Cross Product; Lines and Planes
Lesson 4: Vector-valued Functions
Unit 2: Differentiation in the Multivariable Context
Lesson 5: Functions, Limits, Continuity
Lesson 6: Partial Derivatives; The Chain Rule
Lesson 7: Tangent Planes; Directional Derivatives
Lesson 8: Local and Absolute Extrema
Lesson 9: Optimization
Unit 3: Integration in the Multivariable Context
Lesson 10: Double and Triple Integrals Over Rectangular Regions
Lesson 11: Double and Triple Integrals Over General Regions
Lesson 12: Double and Triple Integrals in Polar and Spherical Coordinates
Unit 4: Vector Calculus
Lesson 13: Scalar Line Integrals
Lesson 14: Parametric Surfaces
Lesson 15: Scalar Surface Integrals
Lesson 16: Vector Line Integrals; Green's Theorems
Differential Equations w/Applied Linear Algebra (Math 215)
Lesson 0: Introduction to ODEs
Lesson 1: First-Order Linear ODEs
Lesson 2: Separable ODEs
Capstone 1: FODEs
Lesson 3: Second-Order Linear ODEs
Lesson 4: Constant-Coefficient SOLDEs
Lesson 5: CC-SOLDEs Continued: The Complex Roots Case
Lesson 6: Non-homogeneous SOLDEs
Lesson 7: Solving Higher-Order Linear ODEs
Capstone 2: SOLDEs and NOLDEs
Lesson 8: Solving Systems of Linear Equations
Lesson 9: Determinants and Cramer's Rule
Lesson 10: Vector Spaces
Lesson 11: Bases and Dimension (of Vector Space)
Lesson 12: The Column Space of a Matrix
Lesson 13: Eigenvalues and Eigenvectors
Capstone 3: Linear Algebra
Lesson 14: Systems of First-Order ODEs
Lesson 15: Solving Systems of First-Order ODEs
Lesson 16: Solving x-dot=Ax Using Eigens: Complex Roots
Lesson 17: The Qualitative Study of ODEs
Lesson 18: Finding Orbits of Plane Autonomous Systems
Lesson 19: Classifying Equilibrium Points for Linear Systems
Capstone 4: Systems of ODEs
Real Analysis (Math 302)
Lesson 1: Introduction to Proofs
Lesson 2: The Fundamental Theorem of Arithmetic
Lesson 3: The Rationals, the Irrationals, and the Reals
Lesson 4: Exploring the Real Numbers
Lesson 5: Functions
Lesson 6: Countable Sets
Lesson 7: Combining Sets: Unions and Intersections
Lesson 8: The Euclidean Space R^n
Lesson 9: The Topology of R^n
Lesson 10: Topology of R^n, Part 2
Lesson 11: The Bolzano-Weierstrass Theorem
Lesson 12: The Lindelof Theorem
Lesson 13: Compactness and the Heine-Borel Theorem
Lesson 14: The Converse of the Heine-Borel Theorem
Lesson 15: Sequences in R^n
Lesson 16: The Relationship Between Adherent Points and Limit Points
Lesson 17: Cauchy Sequences and Completeness
Lesson 18: Limits and Continuity
Lesson 19: An Equivalent Topological Definition of Continuity
Lesson 20: The Extreme Value Theorem; Homeomorphisms
Lesson 21: The Intermediate Value Theorem
Lesson 22: Connectedness
Lesson 23: Uniform Continuity
Lesson 24: Derivatives; Local Extrema
Lesson 25: Rolle’s Theorem, the Mean Value Theorem
Lesson 26: Riemann Integration
Lesson 27: The Fundamental Theorem of Calculus
Complex Analysis (Math 310)
Lesson 1: Complex Numbers and the Complex Plane
Lesson 2: Complex Numbers: Polar Form, Powers, and Roots
Lesson 3: Solving Quadratic Equations in z; Topology of C
Lesson 4: Introduction to Complex Functions and Mappings
Lesson 5: Linear Mappings
Lesson 6: Power Functions
Lesson 7: The Reciprocal Mapping and the Extended Complex Plane
Lesson 8: Complex Limits
Lesson 9: Continuity of Complex Functions
Lesson 10: Complex Differentiability and the Cauchy-Riemann Equations
Lesson 11: The Cauchy-Riemann Equations and Analyticity
Lesson 12: Applications to Fluid Dynamics and Orthogonal Trajectories
Lesson 13: The Complex Logarithm
Lesson 14: Complex Powers
Lesson 15: Complex Trigonometric Functions
Lesson 16: A Review of Line Integrals
Lesson 17: Contour Integrals
Lesson 18: The Cauchy-Goursat Theorem
Lesson 19: Existence of Antiderivatives
Lesson 20: Cauchy’s Integral Formulas
Lesson 21: Consequences of the Cauchy Integral Formulas
Lesson 22: Planar Fluids and their Circulation and Flux
Lesson 23: Sequences and Series in C
Lesson 24: Power Series and Taylor Series
Lesson 25: Laurent Series
Lesson 26: Classifying Isolated Singularities with Laurent Series
Lesson 27: Zeros and Poles
Lesson 28: Cauchy's Residue Theorem
Lesson 29: Evaluating Real Integrals Using the Residue Theorem
Lesson 30: Advanced Integration Techniques Using the Residue Theorem
Lesson 31: Conformal Mappings
Lesson 32: The Riemann Mapping Theorem
Lesson 33: The Riemann Hypothesis, Part 1
Lesson 34: The Riemann Hypothesis, Part 2
Course Videos
Books
Everyday Calculus
Sample Chapter
Interactive Applets
Supplemental Content
Errata
The Calculus of Happiness
Sample Chapter
Interactive Applets
Errata
Calculus Simplified
Sample Chapter
Appendixes and Resources
Interactive Applets
Videos
For Instructors
Errata
Calculus 2 Simplified
Videos
For Instructors
Errata
Review Exercises
Everyday Linear Algebra
Digital Resources
Math Articles
Research & Scholarship
Interactive Applets and Calculators
For Calculus 2 Simplified
How Many Calories Does Your Body Burn Each Day?
How Many Calories Does Your Body Burn per Minute of Exercise?
What’s Your Maximum Heart Rate?
How to Estimate your Total Daily Energy Expenditure
Calculating the (Surprisingly Positive) Effects of Swapping Carbs for Fats
Estimating Your Federal Income Tax Due
Calculating the Monthly Payment on a Loan (Including a Mortgage)
If You Converted Your Rent Payment Into a Mortgage Payment, How Much House
Calculating How Long it’ll Take to Pay Off a Loan
How to Retire Early With the Help of Math
Estimating the Number of Potentially Compatible Partners in Your Area
An Equation for Dividing up Something (Like Pizza) Fairly Between 2 People
How Trigonometry Can Help You Get Better Sleep
Secant & Tangent Lines as Average and Instantaneous Rates of Change
The Mathematics of Coffee Cooling
How Can We Estimate the Greenhouse Gas Emissions Associated With our Diet?
Presentations
Media
CV
Oscar E. Fernandez
The Power of Lines
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