∞ Calculus II

1st and 2nd order ODEs, calculus on curves, differential calculus in Rⁿ, vector functions, multiple integrals, vector fields, Fourier series and transforms. Every topic with step-by-step theory, worked examples and solved exercises.

📋 Formulario

Complete Theory

Worked Examples

Example 1Logistic growth (separable)
Example 2Linear ODE with integrating factor
Example 3Bernoulli equation
Example 4Homogeneous equation
Example 5Exact equation

Exercises with Solutions

Exercise 1SeparableMedium
📋 Problem to solve
Solve the Cauchy problem y′=x/yy'=x/y, y(0)=2y(0)=2.
Exercise 2LinearMedium
📋 Problem to solve
Solve y′−y/x=x2y'-y/x=x^2 for x>0x>0.
Exercise 3BernoulliHard
📋 Problem to solve
Solve the Bernoulli equation y′+y=y3y'+y=y^3.
Exercise 4ExactMedium
📋 Problem to solve
Verify (2xy+y2)dx+(x2+2xy)dy=0(2xy+y^2)dx+(x^2+2xy)dy=0 is exact and find FF.
Exercise 5UniquenessHard
📋 Problem to solve
For y′=∣y∣y'=\sqrt{|y|}, y(0)=0y(0)=0 exhibit two distinct solutions and explain.
Exercise 6HomogeneousMedium
📋 Problem to solve
Solve y′=x+yxy'=\dfrac{x+y}{x} for x>0x>0.
Exercise 7LinearMedium
📋 Problem to solve
RC model: solve q′+q/(RC)=V/Rq'+q/(RC)=V/R with q(0)=0q(0)=0.
Exercise 8ExistenceHard
📋 Problem to solve
Show y′=y2y'=y^2, y(0)=1y(0)=1 blows up in finite time and find the maximal interval.
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Recommended Books

Introductory
Calculus: Early Transcendentals
Stewart, Clegg, Watson
Buy on Amazon →
Intermediate
Multivariable Calculus
Stewart, Watson, Clegg
Buy on Amazon →

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