Calculus: One and Several Variables, with Analytic GeometryA revised and updated presentation of calculus with applications to engineering and the sciences. Changes include an early treatment of the calculus of the trigonometric functions, an increased use of Riemann definition of the integral, the introduction of several numerical techniques, an early chapter on mathematical modeling, expanded and balanced exercise sets, suggested procedures for problem solving, revised proofs, and additional examples. Chapter 13 is contained in both part I and part II. |
Contents
INTRODUCTION | 1 |
DIFFERENTIATION | 28 |
LIMITS AND CONTINUITY | 47 |
Copyright | |
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a₁ angle antiderivative ax² axis bounded C₁ C₂ Calculate chain rule constant converges coordinate cos² cosh curve d₁ decreases defined derivative differential equation diverges domain dot product dx dx ellipse EXAMPLE EXERCISES feet Figure fis continuous formula function f(x given gives gradient hyperbola improper integral inequality integral intersect interval length lim f(x lim h→0 limit local minimum logarithm maximum mean-value theorem minimum P₁ parabola parametrized partial perpendicular plane point of inflection PROBLEM Proof radians radius rate of change real numbers rectangle Riemann sums sec² Section sequence Show sin² sinh Solution surface tan-¹ tangent line theorem triangle trigonometric functions variables vector velocity vertical Vf(x x-axis x₁ xy-plane y-axis y₁ zero ду дх