Lectures overview
The following is a rough lecture plan, together with reading instructions.
Complementary English videos can be found here
Links to an external site.. Lars Filipsson (KTH) has lots of nice Swedish videos for this class.
Links to an external site.
Slides from the lectures are linked in the table, the annotated slides are marked with an a.
Lectures are 2x45 minutes, and we use academic quarter
Links to an external site..
Module 1: Limits and continuity
Lecture a: Introduction to calculus, functions, domain, range, special functions
Lecture b: Limits, squeeze theorem, rules
Lecture c: Continuity
Chapter P Functions, polynomials and trigonometry
Chapter 1.1-1.3, 1.5 Limits
Chapter 1.4 Continuity
Module 2: The derivative
Lecture a: Introduction to derivative, derivative of sin(x)
Lecture b: Rules for computing the derivative
Lecture c: Mean value theorem and higher order derivatives
Chapter 2.1-2.5 Definition, differentiation rules
Chapter 2.6-2.9 Mean Value Theorem, implicit differentiation
Module 3: Transcendental functions
Lecture a: Inverse functions, exponential function, log, their derivatives
Lecture b: Inverse trig, and their derivatives. Brief intro to diff. equations.
Lecture c: Differential equations
Chapter 3.1 Inverse functions
Chapter 3.2-3.4 The natural logarithm
Chapter 3.5-3.6 Inverse trigonometric functions
Chapter 3.7, 18.6 ODE
Module 4: Applications of differentiation and Taylor polynomials
Lecture a: Drawing graphs, critical points, asymptotes
Lecture b: Finding minimum and maximum
Lecture c: l'Hospitals rule, Taylor series
Chapter 4.1, 4.3 Applications
Chapter 4.4-4.8 Extreme values, curve sketching
Chapter 4.9-4.10 Linear approximation and Taylor polynomials
Module 5: Integrals
Lecture a: Introduction to integration, properties, fundamental theorem
Lecture b: Basic integration, substitution, integration by parts
Lecture c: Integration of rational functions, partial fraction decomposition, area.
Chapter 5.1-5.4 Definition and properties
Chapter 2.10, 5.5 The fundamental theorem
Chapter 5.6-5.7, 6.1-6.2 Integration techniques
Module 6: Applications of integration, arc length
Lecture a: Improper integrals, comparison theorem, volume
Lecture b: Computing volume of sphere, cylinder method, arc length, rotation area
Lecture c: Parametric curves, (arc-length and area)
Chapter 6.5 Improper integrals
Chapter 7.1-7.2 Solids of revolution
Chapter 7.3, 8.2, 8.4 Arc length
Module 7: Series
Lecture a: Series
Lecture b: Geometric series, comparison theorems, root theorem.
Lecture c: Taylor and Maclaurin series, uniqueness, convergence
Chapter 9.1-9.3 Series
Chapter 9.6 Taylor and Maclaurin series