Roberto's Math Notes
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  • Calculus
    • Prerequisites for Calculus >
      • Prerequisite algebra and geometry formulae
      • 1 Algebra
      • 2 Functions
      • 3 Transcendental functions
      • 4 Special functions
    • Differential calculus >
      • 1 Limits and continuity
      • 2 Resolving indeterminate forms
      • 3 Definition of derivative
      • 4 Basic differentiation rules
      • 5 Derivatives of transcendental functions
      • 6 Derivatives of other types of functions
      • 7 Linear approximation methods
      • 8 Graphical analysis
      • 9 Word problems
    • Integral calculus >
      • 1: Indefinite integrals
      • 2: Integration methods
      • 3: Basics of ODE's
      • 4: Definite integrals and the FTC
      • 5: Basic applications of integration
      • 6: Improper and approximate integration >
        • Basic differentiation and integration formulae
    • Infinite series >
      • 1: Sequences and series
      • 2: Convergence tests
      • 3: Power series
  • Linear Algebra
    • 1: Geometric vectors
    • 2: Euclidean vectors
    • 3: Linear systems and matrices
    • 4: Matrix algebra
    • 5: Determinants
    • 6: Lines, planes and other straight objects
    • 7: Subspaces
    • 8: Linear transformations
    • 9: Orthogonality
    • 10: Eigenvalues and diagonalization
    • 11: Complex numbers
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Chapter 1: Indefinite integrals
i1-1_antiderivatives_and_indefinite_integrals.pdf
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i1-2_terminology_and_notation_for_indefinite_integrals.pdf
File Size: 340 kb
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i1-3_basic_integration_formulae.pdf
File Size: 485 kb
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Chapter 2: Methods of integration

i2-1_integration_by_substitution.pdf
File Size: 317 kb
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i2-2_integration_by_parts_theory_aspects.pdf
File Size: 369 kb
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i2-3_integration_by_parts_with_two_visible_factors.pdf
File Size: 346 kb
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i2-4_integration_by_parts_with_a_single_visible_factor.pdf
File Size: 424 kb
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i2-5_integration_by_parts_with_cycling_steps.pdf
File Size: 286 kb
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i2-6_reduction_formulae_through_integration_by_parts.pdf
File Size: 178 kb
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i2-7_trigonometric_integrals_by_basic_methods.pdf
File Size: 238 kb
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i2-8_trigonometric_integrals_by_advanced_methods.pdf
File Size: 371 kb
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i2-9_integration_by_inverse_substitution_using_sine.pdf
File Size: 368 kb
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i2-10_integration_by_inverse_substitution_using_secant.pdf
File Size: 185 kb
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i2-11_integration_by_inverse_substitution_using_tangent.pdf
File Size: 308 kb
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i2-12_integration_by_inverse_substitution_using_hyperbolics.pdf
File Size: 307 kb
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i2-13_partial_fractions_preparation.pdf
File Size: 369 kb
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i2-14_partial_fractions_with_non_repeated_linear_factors.pdf
File Size: 447 kb
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i2-15_partial_fractions_with_non_repeated_quadratic_factors.pdf
File Size: 328 kb
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i2-16_partial_fractions_general_case.pdf
File Size: 369 kb
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Chapter 3: Basics of differential equations

i3-1_introduction_to_ode.pdf
File Size: 362 kb
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i3-2_exponential_models.pdf
File Size: 411 kb
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i3-3_separable_ode.pdf
File Size: 478 kb
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i3-4_special_separable_ode.pdf
File Size: 158 kb
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i3-5_linear_ode.pdf
File Size: 519 kb
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i3-6_euler_method.pdf
File Size: 458 kb
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Chapter 4: Definite integrals and the FTC

i4-1_the_area_problem.pdf
File Size: 275 kb
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i4-2_riemann_sums.pdf
File Size: 378 kb
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i4-3_special_types_of_riemann_sums.pdf
File Size: 403 kb
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i4-4_definite_riemann_integral.pdf
File Size: 399 kb
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i4-5_general_properties_of_definite_integrals.pdf
File Size: 503 kb
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i4-6_ftc_theoretical_version.pdf
File Size: 790 kb
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i4-7_ftc_practical_version.pdf
File Size: 378 kb
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i4-8_change_of_variables_and_the_ftc.pdf
File Size: 356 kb
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Chapter 5:Basic applications of integrals

i5-1_the_four_step_process_for_building_integrals.pdf
File Size: 180 kb
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i5-2_areas_between_curves.pdf
File Size: 1127 kb
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i5-3_arc_length.pdf
File Size: 349 kb
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i5-4_areas_of_surfaces_of_revolution.pdf
File Size: 285 kb
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i5-5_volumes_by_slicing.pdf
File Size: 416 kb
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i5-6_volumes_by_disks_and_washers.pdf
File Size: 823 kb
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i5-7_volumes_by_shells.pdf
File Size: 157 kb
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i5-8_picking_the_right_method.pdf
File Size: 218 kb
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i5-9_geometric_quantities_for_parametric_curves.pdf
File Size: 410 kb
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i5-10_geometric_quantities_for_polar_curves.pdf
File Size: 401 kb
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i5-11_work_problems.pdf
File Size: 395 kb
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i5-12_fluid_force_problems.pdf
File Size: 249 kb
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Chapter 6: Improper and approximate integration

i6-1_improper_integrals.pdf
File Size: 296 kb
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i6-2_improper_integrals_with_one_issue_at_one_limit.pdf
File Size: 1416 kb
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i6-3_improper_integrals_with_one_discontinuity_between_limits.pdf
File Size: 186 kb
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i6-4_improper_integrals_with_several_improper_features.pdf
File Size: 311 kb
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i6-5_approximate_integration_midpoint_method.pdf
File Size: 153 kb
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i6-6_approximate_integration_trapezoid_method.pdf
File Size: 437 kb
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i6-7_approximate_integration_simpson_method.pdf
File Size: 703 kb
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i6-8_comparing_approximate_integration_methods.pdf
File Size: 182 kb
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