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Alevel Further Mathematics Alevel进阶数学视频全课程，英语讲解 + 双语字幕
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Roots_of_polynomials 9课时1时13分12秒
免费 6572_Relationship_between_roots_and_coefficients_of_a_quadratic_equation_(1)_ExamSolutions_Maths (08:08)
免费 6573_Relationship_between_roots_and_coefficients_of_a_quadratic_equation_(2)_ExamSolutions (07:07)
6574_Roots_of_a_Cubic_Equation_ExamSolutions (04:04)
6575_Finding_a_Cubic_Equation_with_Reciprocal_Roots_of_another_ExamSolutions_maths_problems_answered (08:08)
6576_Roots_of_a_Quartic_Equation_ExamSolutions (08:08)
6577_Roots_of_a_Quartic_Equation_(example)_ExamSolutions (11:11)
6578_Identity_Sum_of_Cubes_of_Roots_of_a_Cubic_Equation_ExamSolutions (09:09)
6579_Identity_Sum_of_Product_Pairs_of_Cubes_of_Roots_ExamSolutions (09:09)
6580_Roots_of_a_Cubic_Equation_(example)_ExamSolutions (08:08)
Mean_Value_of_a_Function 3课时26分26秒
Trigonometric_Function-_T_formula 3课时20分20秒
Series_Standard_Summations 7课时1时7分19秒
免费 6581_Summing_Series_r_and_ar_b (12:12)
6582_Summing_Series_Harder_types_for_r_and_ar_b (11:11)
6583_Series_Sum_of_Squared_Types_r^2 (09:09)
6584_Series_Sum_of_Cube_Types_r^3 (06:06)
6585_Series_Sum_of_Composite_Functions (08:08)
6586_Summing_Series_The_difference_method (14:42)
6587_Difference_Method_factorial_example (05:51)
Proof_by_Mathematical_Induction 18课时2时4分2秒
免费 6588_Mathematical_Induction_Proof_of_r=n_1_2 (07:07)
试看 6589_Proof_by_Induction_Sum_of_series_r^2 (07:07)
6590_Mathematical_Induction_Sum_of_series_r^3 (08:08)
6591_Proof_by_Induction_Sum_of_series_Example (07:07)
6592_Proof_by_Induction_Sum_of_series_Example (06:06)
6593_Proof_by_Induction_FP1_Edexcel_January_2013_Q8(a) (08:08)
6594_Proof_by_Induction_FP1_Edexcel_January_2013_Q8(b) (07:07)
6595_Proof_by_Induction_(Series)_FP1_Edexcel_January_2012_Q6(a) (08:08)
6596_Summing_Series_FP1_Edexcel_January_2012_Q6(b)(c) (05:05)
6597_Mathematical_Induction_Divisibility_Tests_(1) (08:08)
6598_Mathematical_Induction_Divisibility_Tests_(2) (10:10)
6599_Edexcel_Further_Maths_FP1_June_2014_Q9 (06:06)
6600_Edexcel_Further_Maths_June_2010_Q7a (02:02)
6601_Edexcel_Further_Maths_June_2010_Q7b (04:04)
6602_Mathematical_Induction_Matrix_Multiplication_1 (06:06)
6603_Mathematical_Induction_Matrix_Multiplication_2 (10:10)
6604_Proof_by_Induction_Recurrence_Relation_Further_Maths_FP1_Edexcel_June_2013_Q9_a (05:05)
6605_Proof_by_Induction_Matrices_Further_Maths_FP1_Edexcel_June_2013_Q9_b (08:08)
Vectors: Scalar Product & Vector Equations of lines 14课时1时50分19秒
免费 6861_Vectors_Scalar_or_Dot_Product (10:10)
免费 6862_Scalar_Product_Example (08:08)
6863_Test_for_Perpendicular_Vectors_3D_Scalar_Product (05:05)
6864_Scalar_Product_Perpendicular_Vectors_Example (06:06)
6865_Vectors_Equation_of_a_Line_Introduction (09:09)
6866_Sketching_3D_vector_problems_lines_and_points (04:04)
6867_Vector_Equation_of_a_Line_Example_1 (04:04)
6868_Vectors_equation_of_a_line_through_two_points (07:07)
6869_Vectors_Angle_between_two_lines_given_their_equations (05:05)
6870_Vectors_Conditions_for_lines_to_be_parallel (10:10)
6871_Vectors_Intersecting_and_Skew_Lines (12:12)
6872_Vectors_Closest_point_Shortest_distance_to_a_line (11:11)
6873_Shortest_distance_of_a_point_to_a_line (08:08)
6886_Vectors_Cartesian_Equation_of_a_Line_in_3D (09:40)
Complex Numbers 56课时8时5分43秒
免费 6799_Complex_Numbers_What_are_they_Imagine_no_more. (13:13)
免费 6800_Complex_Numbers_Addition_Subtraction_and_Multiplication (13:13)
免费 6801_Complex_Numbers_Complex_Conjugates (05:05)
免费 6802_Complex_Numbers_Division_Example (05:05)
免费 6803_Complex_Numbers_The_Argand_Diagram (07:07)
6804_Complex_Numbers_Examples (05:05)
6805_Complex_Numbers_Modulus_and_Argument (16:16)
6806_Complex_Numbers_Equations_Equating_real_imag._parts (12:12)
6807_Complex_numbers_Finding_Square_roots_of (12:12)
6808_Complex_Numbers_Roots_of_a_quadratic_equation_conjugate_pairs (09:09)
6809_Complex_Numbers_Roots_of_a_cubic_equation (14:14)
6810_Complex_Numbers_Roots_of_a_quartic_equation (14:14)
6811_Edexcel_FP1_Further_Maths_June_2014_Q1_a (02:02)
6812_Edexcel_FP1_Further_Maths_June_2014_Q1_b (04:04)
6813_Complex_Number_Operations_Further_Maths_FP1_Edexcel_June_2013_Q7_a_b (06:06)
6814_Complex_Number_Operations_Further_Maths_FP1_Edexcel_June_2013_Q7_c (04:04)
6815_Argument_of_a_Complex_Number_Further_Maths_FP1_Edexcel_June_2013_Q7_d (03:03)
6816_Complex_Numbers_FP1_Edexcel_January_2013_Q2 (07:07)
6817_Complex_Numbers_FP1_Edexcel_January_2012_Q1 (08:08)
6818_Complex_Numbers_FP1_Edexcel_January_2011_Q7 (09:09)
6819_Complex_Numbers_Reflection_in_the_Real_Axis (02:02)
6820_Example_to_try_on_Reflecting_a_Complex_Number_in_the_Real_Axis (03:03)
6821_Complex_Numbers_roots_FP1_Edexcel_January_2012_Q5 (08:08)
6822_Complex_Numbers_Roots_FP1_Edexcel_January_2013_Q5 (05:05)
6823_Roots_of_a_Cubic_Equation_Further_Maths_FP1_Edexcel_June_2013_Q3 (05:05)
6824_Edexcel_FP1_Further_maths_June_2014_Q3 (06:06)
6825_Complex_Numbers_Mod_Arg_form_r_cos_x_isin_x (15:15)
6826_Complex_Numbers_Exponential_Form_or_Euler_s_Form (09:09)
6827_Multiplication_Rule_for_the_Mod_Arg_of_two_Complex_Numbers (07:07)
6828_Division_Rule_for_the_Mod_Arg_of_two_Complex_Numbers (09:09)
6829_Multiplication_Division_of_Complex_Numbers_in_Mod_Arg_form_Examples (11:11)
6830_Mod_Arg_of_Complex_Numbers_Further_Maths_FP2_Edexcel_June_2013_Q2 (05:05)
6831_Complex_Numbers_de_Moivre_s_Theorem (04:04)
6832_Using_de_Moivre_s_Theorem_Example_1 (05:05)
6833_Using_de_Moivre_s_Theorem_Example_2 (09:09)
6834_using_de_Moivre_s_theorem_to_express_sin_n_and_cos_n_in_terms_of_sin_and_cos (11:11)
6835_Example_using_de_Moivre_s_theorem_Trig._identities (10:10)
6836_Exam_Question_FP2_Further_Maths_June_2014_Q4_a (05:05)
6837_Edexcel_FP2_Further_Maths_June_2014_Q4_b (03:03)
6838_Exam_Question_FP2_Edexcel_June_2011_Q7_a (07:07)
6839_Trig_Equation_FP2_Edexcel_June_2011_Q7_b (07:07)
6840_Another_identity_using_de_Moivre_s_theorem (07:07)
6841_Powers_of_cos_expressed_in_multiple_angles (09:09)
6842_Odd_Powers_of_sin_expressed_in_multiple_angles (09:09)
6843_Even_Powers_of_sin_expressed_in_multiple_angles (06:06)
6844_Complex_Numbers_Cube_Roots_of_1_unity (19:19)
6845_Complex_Numbers_How_to_find_the_nth_root (14:14)
6846_Mod_Arg_form_of_a_Complex_Number_FP2_Edexcel_June_2012_Q3_a (04:04)
6847_4th_Roots_of_a_complex_number_FP2_Edexcel_June_2012_Q3_b (07:07)
6848_Loci_in_the_Complex_Plane_Circle (11:11)
6849_Complex_Numbers_Loci_Perpendicular_bisector (13:13)
6850_Complex_Numbers_Loci_Half_lines (11:11)
6851_Complex_Numbers_Loci_Regions (10:10)
6852_Complex_Numbers_Loci_FP2_Edexcel_June_2012_Q8_a (06:06)
6853_FP2_Edexcel_June_2012_Q8_b_c (09:09)
6854_Complex_numbers_Further_Maths_IB_HL_Specimen_questions (21:21)
Polar Coordinates & Equations 15课时1时56分55秒
免费 6887_Polar_Coordinates_Defining_the_position_of_a_point (09:09)
免费 6888_Cartesian_to_Polar_Coordinates_Exercise (10:10)
6889_Polar_to_Cartesian_Coordinates_(Exercise) (09:09)
6890_Converting_Polar_Curves_to_Cartesian_Form (11:11)
6891_Converting_Cartesian_Curves_to_Polar_Form (11:11)
6892_Polar_Graphs_the_Spiral (05:05)
6893_Polar_Curves_Half_Lines (03:03)
6894_Polar_Curves_Circles_and_Arcs (03:03)
6895_Polar_Curves_Cardioid (06:06)
6896_Polar_Curves_r=asin2(theta) (04:04)
6897_Area_bounded_by_a_Polar_Curve (04:04)
6898_Polar_Curves_Area_bounded_by_a_Cardioid (09:09)
6899_Area_of_a_Loop_in_a_Polar_Curve (06:06)
6900_Tangents_to_a_Polar_Curve_Parallel_to_the_Initial_Line (11:11)
6901_Tangents_to_a_Polar_Curve_Perpendicular_to_the_Initial_Line (14:14)
Matrices 22课时1时59分58秒
免费 6619_Matrices_Introduction (04:04)
免费 6620_Matrices_Addition_Subtraction_and_Scalar_Multiplication (06:06)
6621_Matrices_Matrix_Multiplication (20:20)
6622_Matrices_Identity_and_Inverse_of_a_2x2_Matrix (12:12)
6623_Singular_Matrix_Example (03:03)
6624_Solving_a_Matrix_Equation (04:04)
6625_Matrix_Identity_Example (05:05)
6626_Matrices_Transposing_Matrices_and_Symmetric_Matrices (03:03)
6627_Determinant_of_a_3x3_Matrix (10:10)
6628_Determinant_of_a_3x3_matrix_Example_1 (01:01)
6629_Determinant_of_a_3x3_matrix_Example_2 (01:01)
6630_Determinant_of_a_3x3_matrix_Example_3 (01:01)
6631_Determinant_of_a_3x3_matrix_Example_4 (01:01)
6632_Determinant_of_a_3x3_matrix_Example_5 (01:01)
6633_Determinant_of_a_3x3_matrix_Example_6 (01:01)
6634_Matrices_Minors_of_elements_in_a_3x3_matrix (04:04)
6635_Matrices_Finding_the_cofactor_matrix (03:03)
6636_Matrices_Inverse_of_a_3x3_matrix (06:06)
6637_Matrices_Working_with_Inverse_Matrices_Example (06:06)
6638_Inverse_Matrices_on_a_Casio_ClassWiz_Calculator (04:04)
6639_Simultaneous_Equations_Matrix_Method (09:09)
6640_Solution_of_3_linear_simultaneous_equations_by_matrices (13:13)
Matrix_Linear_Transformation 15课时1时50分49秒
免费 6641_Transformation_Matrices_Rotation_90_degrees (07:07)
免费 6642_Transformation_Matrices_Rotation_180_degrees (06:06)
6643_Transformation_Matrices_Rotation_270_degrees (06:06)
6644_Transformation_Matrices_Rotation_theta_degrees (08:08)
6645_Transformation_Matrices_Reflection_x_axis (05:05)
6646_Transformation_Matrices_Reflection_y_axis (05:05)
6647_Transformation_Matrices_Reflection_the_line_y=x (05:05)
6648_Transformation_Matrices_Reflection_the_line_y=_x (05:05)
6649_Transformation_Matrices_Enlargement_scale_factor_k_positive (06:06)
6650_Transformation_Matrices_Enlargement_scale_factor_k_negative (07:07)
6651_Matrix_Transformations_Test (17:17)
6652_Combining_Matrix_Transformations (09:09)
6653_Matrices_Reversing_a_transformation (06:06)
6654_Determinant_of_a_matrix_as_the_area_scale_factor (06:06)
6655_Proof_Determinant_of_a_matrix_as_the_area_scale_factor (11:11)
Taylor Series 4课时34分31秒
Maclaurin_Series 5课时38分38秒
Calculus of Inverse Trigonometric Functions 12课时1时21分20秒
免费 6874_Differentiating_inverse_sin_x_a (09:09)
6875_Differentiating_inverse_cos_x_a (09:09)
6876_Differentiating_inverse_tan_x_a (07:07)
6877_Differentiating_Inverse_Trig_Functions_Example_1 (03:03)
6878_Differentiating_Inverse_Trig_Functions_Example_2 (07:07)
6879_How_to_differentiate_Inverse_Trig_Functions_Example_3 (04:04)
6880_Standard_Integrals_1_a_2_x_2_and_1_root_a_2_x_2 (08:08)
6881_Integrals_which_require_completing_the_square (06:06)
6882_Integration_using_completing_the_square_arctan_type_2 (07:07)
6883_Integration_using_completing_the_square_arcsin_type_2 (06:06)
6884_How_to_integrate_1_root_a_2_x_2_with_limits (07:07)
6885_How_to_integrate_1_a_2_x_2_with_limits (07:07)
Hyperbolic_Functions & its Differentiation 19课时2时44分42秒
免费 6902_Hyperbolic_Functions_Definitions_ExamSolutions (09:09)
免费 6903_Graphs_of_sinh_x_cosh_x_and_tanh_x_ExamSolutions (06:06)
6904_Graphs_of_sech_x_cosech_x_and_coth_x_ExamSolutions (10:10)
6905_Graphs_of_Inverse_Hyperbolic_Functions_ExamSolutions (12:12)
6906_arsinh(x)_as_a_natural_logarithm_ExamSolutions (07:07)
6907_arcosh(x)_as_a_natural_logarithm_ExamSolutions (11:11)
6908_artanh(x)_as_a_natural_logarithm_ExamSolutions (07:07)
6909_Solving_simple_Hyperbolic_Equations_using_a_Casio_Calculator_ExamSolutions (15:15)
6910_Solving_hyperbolic_equations_using_identities_ExamSolutions (09:09)
6911_Solving_Hyperbolic_Equations_using_Exponentials_ExamSolutions (08:08)
6912_Osborns_Rule_for_Hyperbolic_Identities_ExamSolutions (10:10)
6913_Proof_of_the_differentials_of_sinh_cosh_and_tanh_x_ExamSolutions (06:06)
6914_Differentiating_hyperbolic_functions_containing_sinh_cosh_tanh(x)_ExamSolutions (07:07)
6915_Proof_of_the_differentials_of_cosech_sech_and_coth_x_ExamSolutions (09:09)
6916_Differentiating_hyperbolic_functions_containing_sech_cosech_coth(x)_ExamSolutions (08:08)
6917_Differentiating_hyperbolic_functions_(short_exercise)_ExamSolutions (08:08)
6918_Hyperbolic_Functions_How_to_differentiate_arsinh_(x_a)_ExamSolutions (07:07)
6919_Hyperbolic_Functions_How_to_differentiate_artanh_(x_a)_ExamSolutions (06:06)
6920_Hyperbolic_Functions_How_to_differentiate_arcosh_(x_a)_ExamSolutions (07:07)
Improper_Integrals 2课时12分8秒
6617_Convergent_Integrals (08:08)
6618_Divergent_Integrals (03:03)
Volumes_of_Revolution 6课时43分43秒
免费 6606_Volume_of_Revolution_about_the_x_axis_1 (05:05)
6607_Volumes_of_Revolution (08:08)
6608_Volume_of_Revolution_about_the_x_axis_between_curves_2 (08:08)
6609_Volume_of_Revolution_about_the_y_axis_1 (05:05)
6610_Volume_of_Revolution_about_the_y_axis_between_curves_2 (08:08)
6611_Volumes_of_Revolution_for_Parametric_Equations_x_axis (09:09)
Differential Equations 17课时2时10分8秒
免费 6921_Differential_Equations_Exact_Type (08:08)
免费 6922_Integrating_factor_Differential_Equations (11:11)
6923_Differential_Equations_Integrating_factor_type_(Examples) (11:11)
6924_Differential_Equations_Substitution_Type_(1) (11:11)
6925_Differential_Equations_Substitution_Type_(2) (11:11)
6926_2nd_Order_Linear_Differential_Equations_Auxillary_Equation_Introduction (05:05)
6927_2nd_Order_Linear_Differential_Equations_Auxillary_Equation_Real_Different_Roots (03:03)
6928_2nd_Order_Linear_Differential_Equations_Auxillary_Equation_Equal_Roots (03:03)
6929_2nd_Order_Linear_Differential_Equations_Auxillary_Eqn_Imaginary_Roots (05:05)
6930_2nd_Order_Linear_Differential_Equations_P.I._=_Constant (07:07)
6931_2nd_Order_Linear_Differential_Equations_P.I._=_Linear_type (06:06)
6932_2nd_Order_Linear_Differential_Equations_P.I._=_Quadratic_type (09:09)
6933_2nd_Order_Linear_Differential_Equations_P.I._=_Exponential_type (05:05)
6934_2nd_Order_Linear_Differential_Equations_P.I._=_trig_type (10:10)
6935_Special_Case_Particular_Integral_(k)_2nd_Order_Linear_Differential_Equation (05:05)
6936_Special_Case_Particular_Integral_(Exp)_2nd_Order_Linear_Differential_Equation (08:08)
6937_2nd_Order_Linear_Differential_Equations_Particular_Solutions (10:10)
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