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Calculus for Engineers and Scientists
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Calculus for Engineers and Scientists
1
Limits and continuity
Limits and one-sided limits
1.1
Limit laws and algebraic methods
1.2
Squeeze theorem and trigonometric limits
1.3
Infinite limits, limits at infinity and asymptotes
1.4
Continuity and discontinuities
1.5
Intermediate value theorem
1.6
Problems
1.7
2
Derivative foundations
Definition and geometry of the derivative
2.1
Differentiation rules
2.2
Chain rule
2.3
Derivatives as functions and higher derivatives
2.4
Problems
2.5
3
Elementary functions and differentiation techniques
Trigonometric derivatives
3.1
Inverse functions and inverse trigonometric derivatives
3.2
Exponential, logarithmic and hyperbolic functions and their derivatives
3.3
Implicit differentiation
3.4
Logarithmic differentiation
3.5
Problems
3.6
4
Applications of derivatives
Linear approximation and differentials
4.1
Related rates
4.2
Extreme values and critical numbers
4.3
Rolle’s theorem and mean value theorem
4.4
Increasing, decreasing and concavity
4.5
Indeterminate forms and l’Hôpital’s rule
4.6
Curve sketching
4.7
Applied optimization
4.8
Problems
4.9
5
Integral foundations
Antiderivatives and indefinite integrals
5.1
Area and Riemann sums
5.2
Definite integrals and their properties
5.3
Fundamental theorem of calculus: differentiating accumulation
5.4
Fundamental theorem of calculus: evaluating definite integrals
5.5
Basic integration formulas
5.6
Problems
5.7
6
Integration techniques
Substitution
6.1
Integration by parts
6.2
Trigonometric substitution
6.3
Problems
6.4
7
Integral applications and improper integrals
Net change and average value
7.1
Areas between curves
7.2
Improper integrals over unbounded intervals
7.3
Improper integrals with unbounded integrands
7.4
Problems
7.5
8
Sequences and power series
Sequences and convergence
8.1
Infinite series and geometric series
8.2
Convergence tools for power series
8.3
Power series: radius and interval of convergence
8.4
Operations on power series
8.5
Problems
8.6
9
Taylor approximation and Taylor series
Taylor and Maclaurin polynomials
9.1
Taylor’s theorem and approximation error
9.2
Taylor and Maclaurin series
9.3
Problems
9.4
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