Calculus 2
The Calculus 2 online course helps you master core integration techniques and their applications. You will then explore other key aspects of Mathematical functions. The skills developed in this course are important for students wishing to subsequently pursue Math, science, technology or engineering. View our classroom or learn more below and start your Calculus 2 course access.
Calculus 2 Curriculum
- Antiderivatives (7:42)
- Antiderivatives and Integration (10:10)
- Notation for Integration (12:19)
- The Power Rule (14:39)
- Integratable Form (10:40)
- Indefinite and Definite Integrals (6:46)
- Evaluating Definite Integrals (13:33)
- Riemann Sums (9:52)
- Integrals and Riemann Sums (7:42)
- The Fundamental Theorem of Calculus (13:01)
- Practice Questions
- Integration by U-Substitution (18:09)
- The Reverse Chain Rule (11:06)
- Integration by Parts (17:59)
- Integration by Parts for Definite Integrals (14:49)
- Integration using Partial Fractions (35:20)
- Integrating the Sine and Cosine Functions (8:46)
- Integrating the Tangent Function (7:49)
- Integrals Involving Exponential and Logarithmic Functions (11:17)
- Improper Integrals (16:29)
- Evaluating Improper Integrals of the Form [a, infinity) (11:33)
- Evaluating Improper Integrals of the Form (- infinity, infinity) (13:46)
- Evaluating Improper Integrals - Discontinuous at ‘a’ or ‘b’ (10:47)
- Improper Integrals – Discontinuous in the interval (a, b) (14:50)
- Practice Questions
- Finding the Area Under a Curve (16:51)
- Finding the Area Between Two Curves (18:59)
- Volumes of Revolution (9:53)
- Volumes of Revolution Around the X-Axis (11:57)
- Volumes of Revolution Around the Y-Axis (16:44)
- Arc Length Using Integration (9:09)
- Evaluating Arc Length Using Integration (19:56)
- Practice Questions
- Parametric Functions (10:14)
- Writing Parametric Functions in Cartesian Form (15:38)
- Differentiating Parametric Functions (13:26)
- Second Derivatives for Parametric Functions (15:30)
- Curves of Parametric Functions (15:52)
- Tangent Lines to Parametric Curves (17:46)
- The Area Under a Parametric Curve (13:42)
- The Arc Length of a Parametric Curve (29:52)
- Volumes of Revolution for Parametric Curves (13:33)
- Surface Area of Revolution for Parametric Curves (11:50)
- Practice Questions
- Polar Co-ordinates (8:35)
- Switching Between Polar and Cartesian Co-ordinates (16:34)
- Graph Sketching for Polar Curves (32:38)
- Tangent Lines to Polar Curves (28:12)
- The Intersection of Polar Curves (20:36)
- The Area Bounded by a Polar Curve (14:43)
- The Arc Length of a Polar Curve (18:48)
- The Surface Area of Revolution of a Polar Curve (16:07)
- Practice Questions
- Partial Sums of an Infinite Series (11:51)
- Sum of an Infinite Series Using Partial Sums (22:26)
- Geometric Series Convergence Test (16:15)
- The Sum of a Geometric Series (16:12)
- Repeating Decimal Problems (7:52)
- Telescoping Series (26:17)
- The Sum of a Convergent Telescoping Series (11:34)
- The Limit and Sum of an Infinite Series (9:28)
- Common Series Results (12:50)
- Practice Questions
- The Integral Convergence Test (17:56)
- The P-Series Test (12:45)
- The Nth Term Test (16:19)
- The Direct Comparison Test (14:19)
- The Limit Comparison Test (15:44)
- The Ratio Test (17:49)
- The Root Test (17:20)
- Absolute and Conditional Convergence (17:19)
- Alternating Series Test (20:20)
- Alternating Series Estimates (12:30)
- Practice Questions
- Starting Power Series (7:18)
- Power Series, Taylor Series and Maclaurin Series (9:49)
- Radius and Interval of Convergence (10:18)
- Multiplying Power Series (14:51)
- Differentiating Power Series (7:43)
- Evaluating Indefinite Integrals for Power Series (10:52)
- Evaluating Definite Integrals for Power Series (10:34)
- Starting Maclaurin Series (16:59)
- Evaluating the Sum of a Maclaurin Series (8:32)
- The Radius and Interval of Convergence of a Maclaurin Series (26:22)
- Writing Indefinite Integrals as an Infinite Series (8:31)
- Approximating Definite Integrals Using an Infinite Series (24:02)
- Starting Taylor Series (13:52)
- The Radius and Interval of Convergence of a Taylor Series (24:33)
- Practice Questions
Who is the Calculus 2 Course For?
Calculus 2 is for students who have experience of Differential Calculus and want to develop similar Integral Calculus skills. Students taking Calculus 2 should have ideally completed a course in Calculus 1. View the CLASSROOM.
What is Taught in Calculus 2?
Core and Advanced Integration Techniques, Applications of Integrals, Parametric & Polar Functions, Sequences & Series, Series Convergence Tests, Power Series. View the full CURRICULUM.
What Will I Take Away From This Course?
Students will master various Integration techniques & applications, and will gain considerable experience of sequences & series. Students practice what they’ve learnt from our instructional videos using carefully designed Calculus 2 worksheets.
How Does Calculus 2 Compare to Calculus 1?
Calculus comes in two flavours. Calculus 2 focuses on Integral Calculus and Calculus 1 focuses on Differential Calculus.
What is the Progression From Calculus 2?
Students are in a strong position to take Vector Calculus, Mathematical Analysis or to apply Calculus in real-world scenarios.
Hi, I’m Gary, and I'll be your instructor for this course in Calculus 2.
I'll be straight with you, I love Math! But I completely get that for most of us it's very challenging, and often frustrating. I'm here to help make it easier for you. I've taught many Calculus 2 students. I understand the sticking points and how to help you develop skills and boost your confidence. I have a BSc Honours degree in Pure Mathematics and have been educated in both the UK and the US. I own and run a private tuition business where I've served many hundreds of Maths students.