pic_cooming_soonCalculus 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.


Dr. Andréa Marchese.

Calculus I (College Calculus)

Calc I Lesson 01 Functions

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 06 Continuity

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 19 Concavity

Calc I Lesson 20 Curve Sketching

Calc I Lesson 21 Optimization

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 20 Arc Length

Calc II Lesson 21 Work

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 02 Vectors

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 06 Planes

Calc III Lesson 07 Cylinders

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 12 Limits

Calc III Lesson 13 Continuity

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 29 Sequences

Calc III Lesson 30 Series

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 02

Calculus I – Lecture 03 – Trigonometry for Calculus

Calculus I – Lecture 04 – Intuitive Beginning – Limits

Calculus I – Lecture 05-06

Calculus I – Lecture 07

Calculus I – Lecture 08 – Trigonometric Functions (new version)

Calculus I – Lecture 09

Calculus I – Lecture 10

Calculus I – Lecture 11

Calculus I – Lecture 12

Calculus I – Lecture 13

Calculus I – Lecture 14

Calculus I – Lecture 15

Calculus I – Lecture 16

Calculus I – Lecture 17

Calculus I – Lecture 18

Calculus I – Lecture 19

Calculus I – Lecture 20

Calculus I – Lecture 21

Calculus I – Lecture 22

Calculus I – Lecture 22-5

Calculus I – Lecture 23

Calculus I – Lecture 24

Calculus I – Lecture 25

Calculus I – Lecture 26

Calculus I – Lecture 27

Calculus I – Lecture 28 – One Dimensional Motion & the Integral

Calculus I – Lecture 29

Calculus I – Lecture 29 Part II – The Definite Integral Applied: Volumes I

Calculus I – Lecture 30

Calculus I – Lecture 30-03

Calculus I – Lecture 30-04

Calculus I – Lecture 31

Calculus I – Lecture 31-06

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

Calculus 2 Lecture 10.5: Calculus of Polar Equations

Numerical Integration With Trapezoidal and Simpson’s Rule

 Open Textbooks:
  1. Guichard: Single Variable Calculus, Early Transcendentals
  2. Guichard: Single Variable Calculus, Late Transcendentals
  3. Boelkins: Active Calculus
  4. Hartman, Heinold, Siemers and Chalishajar: APEX Calculus
  5. Callahan: Calculus in Context
  6. Strang: Calculus
  7. Corral: Vector Calculus
  8. Hartman, et. al: APEX Calculus
Further Reading:
  1. 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

Buy at Amazon.co.uk

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

Buy at Amazon.co.uk

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

Buy at Amazon.co.uk