Calculus I
Read OpenStax: “Calculus I” Online
Onnline Lectures:
Welcome to Calculus I, II & III with Dr. Marchese! I created these videos for use with my hybrid Calculus classes at The City College of New York. They are intended to be complete, time-efficient lessons covering each topic in the Calculus series. (For detailed course descriptions, see http://math.sci.ccny.cuny.edu/course/list .) Special thanks to the Office of the Provost and the Center for Excellence in Teaching and Learning at CCNY for supporting this work with a Technology Grant for Transforming Teaching and Learning. Special thanks also to Prof. Ring and Prof. Cleary for their important contributions to the content of these videos.
Enjoy!
Dr. Andréa Marchese.
Calculus I (College Calculus)
Calc I Lesson 02 Important Functions to Know
Calc I Lesson 03 An Introduction to Limits
Calc I Lesson 04 Calculating Limits
Calc I Lesson 05 The Squeeze Theorem
Calc I Lesson 07 Limits Involving Infinity
Calc I Lesson 08 The Derivative at a Point
Calc I Lesson 09 The Derivative Function
Calc I Lesson 10 Basic Differentiation Formulas
Calc I Lesson 11 The Product and Quotient Rules
Calc I Lesson 12 The Chain Rule
Calc I Lesson 13 Implicit Differentiation
Calc I Lesson 14 Related Rates
Calc I Lesson 15 Linear Approximations and Differentials
Calc I Lesson 16 Maximum and Minimum Values (Absolute Extrema)
Calc I Lesson 17 The Mean Value Theorem
Calc I Lesson 18 Relative Extrema
Calc I Lesson 20 Curve Sketching
Calc I Lesson 22 Antiderivatives
Calc I Lesson 23 Sigma Notation
Calc I Lesson 24 Area Under a Curve
Calc I Lesson 25 The Definite Integral
Calc I Lesson 26 First Fundamental Theorem
Calc I Lesson 27 Indefinite Integrals
Calc I Lesson 28 Second Fundamental Theorem
Calc I Lesson 29 Integration by Substitution
Calculus II (College Calculus)
Calc II Lesson 01 Inverse Functions
Calc II Lesson 02 The Natural Logarithmic Function
Calc II Lesson 03 The Natural Exponential Function
Calc II Lesson 04 General Logarithmic and Exponential Functions
Calc II Lesson 05 The Number e as a Limit
Calc II Lesson 06 Exponential Growth and Decay
Calc II Lesson 07 Inverse Trigonometric Functions
Calc II Lesson 08 Hyperbolic Functions
Calc II Lesson 09 Indeterminate Forms and L’Hospital’s Rule
Calc II Lesson 10 Integration by Parts
Calc II Lesson 11 Trigonometric Integrals
Calc II Lesson 12 Integrals with Trigonometric Substitution
Calc II Lesson 13 Partial Fractions
Calc II Lesson 14 Approximate Integration
Calc II Lesson 15 Improper Integrals
Calc II Lesson 16 The Comparison Theorem for Improper Integrals
Calc II Lesson 17 Areas Between Curves
Calc II Lesson 18 Volumes by Slicing, Including Disks and Washers
Calc II Lesson 19 Volumes by Cylindrical Shells
Calc II Lesson 22 Parametric Curves
Calc II Lesson 23 Calculus with Parametric Curves
Calc II Lesson 24 Polar Coordinates
Calc II Lesson 25 Polar Curves
Calc II Lesson 26 Areas and Lengths in Polar Coordinates
Calc II Lesson 27 Conic Sections
Calc II Lesson 28 Rotated Conics
Calculus III (College Calculus)
Calc III Lesson 01 The Three Dimentional Coordinate System
Calc III Lesson 03 The Dot Product
Calc III Lesson 04 The Cross Product
Calc III Lesson 05 Lines in Three Dimensional Space
Calc III Lesson 08 Quadric Surfaces
Calc III Lesson 09 Vector Valued Functions
Calc III Lesson 10 Parametric Surfaces
Calc III Lesson 11 Functions of Several Variables
Calc III Lesson 14 Partial Derivatives
Calc III Lesson 15 Tangent Planes and Linear Approximations
Calc III Lesson 16 The Chain Rule
Calc III Lesson 17 Dir Deriv and Gradient
Calc III Lesson 18 Relative Extrema and Saddle Points
Calc III Lesson 19 Absolute Extrema
Calc III Lesson 20 Optimization
Calc III Lesson 21 Double Integrals Over Rectangles
Calc III Lesson 22 Double Integrals General Regions
Calc III Lesson 23 Double Integrals in Polar Coordinates
Calc III Lesson 24 Applications of the Double Integral
Calc III Lesson 25 Surface Area
Calc III Lesson 26 Triple Integrals
Calc III Lesson 27 Cylindrical Coordinates
Calc III Lesson 28 Spherical Coordinates
Calc III Lesson 31 Series Convergence Tests
Calc III Lesson 32 Power Series
Calc III Lesson 33 Representing Functions as Power Series
Calc III Lesson 34 Taylor and Maclaurin Series
Calc III Lesson 35 Approximations Using Taylor Polynomials
University Calculus:
Calculus I – Lecture 01 – A Review of Pre-Calculus
Calculus I – Lecture 03 – Trigonometry for Calculus
Calculus I – Lecture 04 – Intuitive Beginning – Limits
Calculus I – Lecture 08 – Trigonometric Functions (new version)
Calculus I – Lecture 28 – One Dimensional Motion & the Integral
Calculus I – Lecture 29 Part II – The Definite Integral Applied: Volumes I
Calculus II:
Calculus 2 Lecture 6.1: The Natural Log Function
Calculus 2 Lecture 6.2: Derivatives of Inverse Functions
Calculus 2 Lecture 6.3: Derivatives and Integrals of Exponential Functions
Calculus 2 Lecture 6.4: Derivatives and Integrals of General Exponential Functions
Calculus 2 Lecture 6.5: Calculus of Inverse Trigonometric Functions
Calculus 2 Lecture 6.6: A Discussion of Hyperbolic Functions
Calculus 2 Lecture 6.7: Evaluating Limits of Indeterminate Forms
Calculus 2 Lecture 7.1: Integration By Parts
Calculus 2 Lecture 7.2: Techniques For Trigonometric Integrals
Calculus 2 Lecture 7.3: Integrals By Trigonometric Substitution
Calculus 2 Lecture 7.4: Integration By Partial Fractions
Calculus 2 Lecture 7.6: Improper Integrals
Calculus 2 Lecture 8.1: Solving First Order Differential Equations By Separation of Variables
Calculus 2 Lecture 9.1: Convergence and Divergence of Sequences
Calculus 2 Lecture 9.2: Series, Geometric Series, Harmonic Series, and Divergence Test
Calculus 2 Lecture 9.3: Using the Integral Test for Convergence/Divergence of Series, P-Series
Calculus 2 Lecture 9.4: The Comparison Test for Series and The Limit Comparison Test
Calculus 2 Lecture 9.5: Showing Convergence With the Alternating Series Test, Finding Error of Sums
Calculus 2 Lecture 9.6: Absolute Convergence, Ratio Test and Root Test For Series
Calculus 2 Lecture 9.7: Power Series, Calculus of Power Series, Ratio Test for Int. of Convergence
Calculus 2 Lecture 9.8: Representation of Functions by Taylor Series and Maclauren Series
Calculus 2 Lecture 9.9: Approximation of Functions by Taylor Polynomials
Calculus 2 Lecture 10.2: Introduction to Parametric Equations
Calculus 2 Lecture 10.3: Calculus of Parametric Equations
Calculus 2 Lecture 10.4: Using Polar Coordinates and Polar Equations
Open Textbooks:
- Guichard: Single Variable Calculus, Early Transcendentals
- Guichard: Single Variable Calculus, Late Transcendentals
- Boelkins: Active Calculus
- Hartman, Heinold, Siemers and Chalishajar: APEX Calculus
- Callahan: Calculus in Context
- Strang: Calculus
- Corral: Vector Calculus
- Hartman, et. al: APEX Calculus
Further Reading:
- Stewart and Busch: Calculus (International Metric Version) Hardcover – 4 Oct 2015
Success in your calculus course starts here! James Stewart’s CALCULUS INTERNATIONAL METRIC EDITION texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, 8E, INTERNATIONAL METRIC EDITION, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course.
- Hardcover: 1368 pages
- Publisher: Brooks/Cole; International Metric ed of 8th Revised ed edition (4 Oct. 2015)
- Language: English
- ISBN-10: 1305266722
- ISBN-13: 978-1305266728
- Product Dimensions: 22.5 x 5.3 x 26.2 cm
2. Ryan: Calculus For DummiesPaperback – 18 Jul 2014
Slay the calculus monster with this user–friendly guide Calculus For Dummies, 2 nd Edition makes calculus manageable—even if you′re one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user–friendly math book leads you step–by–step through each concept, operation, and solution, explaining the “how” and “why” in plain English instead of math–speak. Through relevant instruction and practical examples, you′ll soon learn that real–life calculus isn′t nearly the monster it′s made out to be. Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It′s the logical extension of the algebra, geometry, and trigonometry you′ve already taken, and Calculus For Dummies, 2 nd Edition proves that if you can master those classes, you can tackle calculus and win. Includes foundations in algebra, trigonometry, and pre–calculus concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can′t get away with Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you′ll gain the skills and confidence that make all the difference. Calculus For Dummies, 2 nd Edition provides a roadmap for success, and the backup you need to get there.
- Paperback: 384 pages
- Publisher: John Wiley & Sons; 2nd Edition edition (18 July 2014)
- Language: English
- ISBN-10: 1118791290
- ISBN-13: 978-1118791295
- Product Dimensions: 18.8 x 1.8 x 23.6 cm
3. Ryan: Calculus Workbook For Dummies. Paperback – 14 Sep 2015
Your light–hearted, practical approach to conquering calculus
Does the thought of calculus give you a coronary? You aren′t alone. Thankfully, this new edition of Calculus Workbook For Dummies makes it infinitely easier. Focusing “beyond the classroom,” it contains calculus exercises you can work on that will help to increase your confidence and improve your skills. This hands–on, friendly guide gives you hundreds of practice problems on limits, vectors, continuity, differentiation, integration, curve–sketching, conic sections, natural logarithms, and infinite series.
Calculus is a gateway and potential stumbling block for students interested in pursuing a career in math, science, engineering, finance, and technology. Calculus students, along with math students in nearly all disciplines, benefit greatly from opportunities to practice different types of problems in the classroom and out. Calculus Workbook For Dummies takes you step–by–step through each concept, operation, and solution, explaining the “how” and “why” in plain English, rather than math–speak. Through relevant instruction and practical examples, you′ll soon learn that real–life calculus isn′t nearly the monster it′s made out to be.
- Master differentiation and integration
- Use the calculus microscope: limits
- Analyze common functions
- Score your highest in calculus
Complete with tips for problem–solving and traps to avoid, Calculus Workbook For Dummies is your sure–fire weapon for conquering calculus!
- Paperback: 336 pages
- Publisher: John Wiley & Sons; 2nd Edition edition (14 Sept. 2015)
- Language: English
- ISBN-10: 1119013925
- ISBN-13: 978-1119013921
- Product Dimensions: 20.4 x 1.8 x 25.4 cm